(B) 16.4 m.sec. (B) The number of requests for disk service are not influenced by file allocation method. The number of vertices will be less than or equal to 40,000. Therefore 5/8 work is done by them, = (96/5*5/8) =12 days. (3) Overloaded functions cannot handle different types of objects. Consider an experiment of tossing two fair dice, one black and one red. STEP 1: Create Adjacency Matrix for the given graph. There is an edge between (a, b) and (c, d) if |a – c| ≤ 1 or |b–d| ≤ 1. I believe there are two non-isomorphic spanning trees in K4. The page reference string is :  1 2 3 2 5 6 3 4 6 3 7 3 1 5 3 6 3 4 2 4 3 4 5 1  The number of page faults in LRU and optimal page replacement algorithms are respectively (without including initial page faults to fill available page frames with pages): (A) 9 and 6 (B) 10 and 7 (C) 9 and 7 (D) 10 and 6, At which of the following stage(s), the degeneracy do not occur in transportation problem? (B) The number of requests for disk service are not influenced by file allocation method. 2. to manage changes to one or more of these items. Assume that disk head is initially positioned at cylinder 53 and moving towards cylinder number 0. (A) minimal, maximal (B) minimal, minimal (C) maximal, maximal (D) maximal, minimal, The order of a leaf node in a B+ tree is the maximum number of children it can have. The number of days for which Z worked is. General Properties of Spanning Tree We now understand that one graph can have more than one spanning tree. So, the complete graph with 4 vertices has 4 (4-2) = 16 spanning trees. 4.3 Enumerating all the spanning trees on the complete graph Kn Cayley’s Thm (1889): There are nn-2 distinct labeled trees on n ≥ 2 vertices. Image (A) 2 (B) 4 (C) 5 (D) 6. 1 person 1 day's work = 1/(90 *32) i.e., 1/2880 90 person's 12 day's work = 1/32 * 12 = 3/8 Remaining work =(1- 3/8) = 5/8 150 persons 1 ... 5/96 work is done by them in 1 day . a) 10 days b) 12 days c) 14 days d) 16 days. Show that a spanning tree of the complete graph K 4 is either a depth-first spanning tree or a breadth-first spanning tree. No, although there are graph for which this is true (note that if all spanning trees are isomorphic, then all spanning trees will have the same number of leaves). Don’t stop learning now. 4 2 = 16. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Find the number of hours taken by pipe R to fill the tank if the remaining tank is filled in 14 hours. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. Scoins' formula gives the number of different spanning trees in a complete bipartite graph. Physical memory consists of 32 page frames. The number of edges will be less than or equal to 100,000. R. Onadera, On the number of trees in a complete n-partite graph.Matrix Tensor Quart.23 (1972/73), 142–146. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Find if there is a path of more than k length from a source, Printing all solutions in N-Queen Problem, Warnsdorff’s algorithm for Knight’s tour problem, The Knight’s tour problem | Backtracking-1, Count number of ways to reach destination in a Maze, Count all possible paths from top left to bottom right of a mXn matrix, Print all possible paths from top left to bottom right of a mXn matrix, Unique paths covering every non-obstacle block exactly once in a grid, Tree Traversals (Inorder, Preorder and Postorder). Each spanning tree is associated with a two-number sequence, called a Prufer¨ sequence, which will be explained later. List All The Spanning Trees Of The Complete Graph K4 On Labeled Vertices V = {u}, 12, 13, 14). In some cases, it is easy to calculate t(G) directly. The vertex set of G is {(i, j) | 1 ≤ i ≤ 12, 1 ≤ j ≤ 12}. The Questions and Answers of The number of spanning trees for a complete graph with seven vertices isa)25b)75c)35d)22 x 5Correct answer is option 'B'. Theorem 1. What is the average number of bits per symbol for the Huffman code generated from above information? (C) K3,3 or K5 Explanation: Kuratowski’s Theorem: A graph is non-planar if and only if it contains a subgraph that is homeomorphic to either K5 or K3,3. (A) 2 bits per symbol (B) 1.75 bits per symbol (C) 1.50 bits per symbol (D) 1.25 bits per symbol, A process which defines a series of tasks that have the following four primary objectives is known as 1. to identify all items that collectively define the software configuration. (A) M+N-C (B) M-N-C (C) M-N+C (D) M+N+C, The number of function points of a proposed system is calculated as 500. For a connected simple graph G let L(G) denote the maximum number of leaves in any spanning tree of G. Linial conjectured that if G has N vertices and minimum degree k, then ... (B) 16, 14 (C) 16, 4 (D) 14, 4 (C) 28 m.sec. A memory management system has 64 pages with 512 bytes page size. STEP 4: Calculate co-factor for any element. (A) 3 (B) 7 (C) 10 (D) 21, Pipes P, Q and R which fill the tank together in 12 hours are opened for 2hours after which pipe R was closed. So as per the definition, a minimum spanning tree is a spanning tree with the minimum edge weights among all other spanning trees in the graph. The number of days taken by vikram to do the same piece of work.  a) 12 days b) 14 days c) 16 days d) 18 days. The spanning tree is complete. In the above addressed example, n is 3, hence 33−2 = 3 spanning trees are possible. 1. If a graph is a complete graph with n vertices, then total number of spanning trees is n (n-2) where n is the number of nodes in the graph. If the other vertices have degree 1, how many vertices are there in the graph? (c) A complete graph (Kn) has a Hamilton Circuit whenever n≥3 (d) A cycle over six vertices (C6) is not a bipartite graph but a complete graph over 3 vertices is bipartite. The Number of Spanning Trees in Regular Graphs Noga Alon* School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel ABSTRACT Let C(G) denote the number of spanning trees of a graph G.It is shown that there is a function ~(k) that tends to zero as k tends to infinity such that for every connected, Attention reader! (B) 16.4 m.sec. This method is also known as Kirchhoff’s Theorem. A. (d) At a stage when the no. i.e. Griggs, J.R. and M. Wu, Spanning trees in graphs of minimum degree 4 or 5, Discrete Mathematics 104 (1992) 167-183. Which of the following sequences could not be the sequence of nodes examined? (A) 70 (B) 14 (C) 13 (D) 7, Consider a disk queue with request for input/output to block on cylinders  98, 183, 37, 122, 14, 124, 65, 67  in that order. This article is contributed by Kapil Khandelwal. (C) 28 m.sec. If a graph is a complete graph with n vertices, then total number of spanning trees is n(n-2) where n is the number of nodes in the graph. Estimate the effort (E) required to complete the project using the effort formula of basic COCOMO given below: E = a(KLOC)b Assume that the values of a and b are 2.5 and 1.0 respectively. And a complete graph with n vertices has n (n-2) spanning trees. (A) The number of regions – 1 (B) E – N + 1, where E is the number of flow graph edges and N is the number of flow graph nodes. The time taken to service a page fault is 8 m.sec. Which of the following statements is not true about disk-arm scheduling algorithms ? https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem#Proof_outline. It can be applied to complete graphs also. (A) 14, 14 (B) 16, 14 (C) 16, 4 (D) 14, 4, Which of the following statement(s) is/are false? (D) SCAN and C-SCAN algorithms are less likely to have a starvation problem. I think the best way of finding the number of minimum … By using our site, you NOTE- Co-factor for all the elements will be same. Then f(Around - 4) is given by: (A) {(2,0.6), (3,0.3), (6,1), (11,0.3)} (B) {(2,0.6), (3,1), (6,1), (11,0.3)} (C) {(2,0.6), (3,1), (6,0.6), (11,0.3)} (D) {(2,0.6), (3,0.3), (6,0.6), (11,0.3)}, Pipes P, Q and R which fill the tank together in 12 hours are opened for 2hours after which pipe R was closed. Let A and B be two fuzzy integers defined as: A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)} B={(10,0.5), (11,1), (12,0.5)} Using fuzzy arithmetic operation given by Image (A) {(11,0.8), (13,1), (15,1)} (B) {(11,0.3), (12,0.5), (13,1), (14,1), (15,1), (16,0.5), (17,0.2)} (C) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,1), (16,0.5), (17,0.2)} (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}, Compute the value of adding the following two fuzzy integers: A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)} B = {(0.5,11), (1,12), (0.5,13)} Where fuzzy addition is defined as μA+B(z) = maxx+y=z (min(μA(x), μB(x))) Then, f(A+B) is equal to (A) {(0.5,12), (0.6,13), (1,14), (0.7,15), (0.7,16), (1,17), (1,18)} (B) {(0.5,12), (0.6,13), (1,14), (1,15), (1,16), (1,17), (1,18)} (C) {(0.3,12), (0.5,13), (0.5,14), (1,15), (0.7,16), (0.5,17), (0.2,18)} (D) {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)}, Given a Non-deterministic Finite Automation (NFA) with states p and r as initial and final states respectively transition table as given below Image The minimum number of states required in Deterministic Finite Automation (DFA) equivalent to NFA is (A) 5 (B) 4 (C) 3 (D) 2, Suppose the function y and a fuzzy integer number around -4 for x are given as y=(x-3)2+2 Around -4={(2,0.3), (3,0.6), (4,1), (5,0.6), (6,0.3)} respectively. (C) P – 1, where P is the number of predicate nodes in the flow graph G. (D) P + 1, where P is the number of predicate nodes in the flow graph G. (D) P + 1, where P is the number of predicate nodes in the flow graph G. Consider an undirected graph G where self-loops are not allowed. i.e. 2! 4. to ensure that software quality is maintained as the configuration evolves over time. Assume that disk head is initially positioned at cylinder 53 and moving towards cylinder number 0. Spanning trees in a bipartite graph K m,n is equal to m (n-1) * n (m-1). Any spanning tree of the graph will also have \(v\) vertices, and since it is a tree, must have \(v-1\) edges. Vikram is 75% more efficient than vinay. then G has a spanning f ‐tree. (A) Best first search (B) Goal stack planning (C) Alpha-beta pruning procedure (D) Min-max search, The octal number 326.4 is equivalent to (A) (214.2)10 and (D6.8)16 (B) (212.5)10 and (D6.8)16 (C) (214.5)10 and (D6.8)16 (D) (214.5)10 and (D6.4)16, The mean of 8 article was found to be 15. As the complete graph on nvertices has n(n 2) spanning trees, our algorithm has to operate on numbers of this magnitude. For example, the value of n is 5 then the number of spanning trees would be equal to 125. (D) 14 m.sec. There is only one minimum spanning tree in the graph where the weights of vertices are different. These resources are shared by three processes P1, P2 and P3 which have peak demands of 2, 5 and 7 resources respectively. (A) Complete graph (B) Hamiltonian graph (C) Euler graph (D) None of the above, The number of candidates writing three different entrance exams is in the ratio 4:5:6. 1 Background 1.1 Trees and Spanning Trees The types of graphs we will focus on are trees and spanning trees. See the answer. There is a proposal to increase these numbers of candidates by 40%, 60% and 85% respectively. Several proofs of this formula The number of spanning trees of Kand K,207 can be found in [3]. (b) While obtaining an initial solution, we may have less than m + n -1 allocations. (A) 22 / 36 (B) 12 / 36 (C) 14 / 36 (D) 6 / 36, Let E1 and E2 be two entities in E-R diagram with simple single valued attributes. (a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree. Theorem 2. (A) 925, 221, 912, 245, 899, 259, 363, 364 (B) 3, 400, 388, 220, 267, 383, 382, 279, 364 (C) 926, 203, 912, 241, 913, 246, 364 (D) 3, 253, 402, 399, 331, 345, 398, 364Â. (C) Shift step that advances in the input stream by K(K = 2) symbols and Reduce step that applies a completed grammar rule to form a single tree. A) 16 B) 14 C) 20 D) 42, A process which defines a series of tasks that have the following four primary objectives is known as 1. to identify all items that collectively define the software configuration. So, spanning trees in complete graph K 4 will be 4 (4 – 2). (c) A complete graph (Kn) has a Hamilton Circuit whenever n≥3 (d) ... a bipartite graph but a complete graph over 3 vertices is bipartite. (A) Two (B) Three (C) Four (D) Five. Adjacency Matrix for the above graph will be as follows: After applying STEP 2 and STEP 3, adjacency matrix will look like. Note that all graphs are assumed to be labeled. Total number of Spanning Trees in a Graph, Total number of Spanning trees in a Cycle Graph, Number of spanning trees of a weighted complete Graph, Problem Solving for Minimum Spanning Trees (Kruskal’s and Prim’s), Maximum Possible Edge Disjoint Spanning Tree From a Complete Graph, Program to find total number of edges in a Complete Graph, Applications of Minimum Spanning Tree Problem, Boruvka's algorithm for Minimum Spanning Tree, Kruskal's Minimum Spanning Tree using STL in C++, Reverse Delete Algorithm for Minimum Spanning Tree, Minimum spanning tree cost of given Graphs, Find the weight of the minimum spanning tree, Find the minimum spanning tree with alternating colored edges, Minimum Spanning Tree using Priority Queue and Array List, Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2, Prim’s Minimum Spanning Tree (MST) | Greedy Algo-5, Spanning Tree With Maximum Degree (Using Kruskal's Algorithm), Maximum Spanning Tree using Prim’s Algorithm, Count total ways to reach destination from source in an undirected Graph, Size of the Largest Trees in a Forest formed by the given Graph, Maximum number of edges that N-vertex graph can have such that graph is Triangle free | Mantel's Theorem, Graph implementation using STL for competitive programming | Set 2 (Weighted graph), Data Structures and Algorithms – Self Paced Course, Ad-Free Experience – GeeksforGeeks Premium, We use cookies to ensure you have the best browsing experience on our website. Geometrically K3 forms the edge set of a triangle, K4 a tetrahedron, etc. are solved by group of students and teacher of Computer Science Engineering (CSE), which is also the largest student community of Computer Science Engineering (CSE). (1) Compiler sets up a separate function for every definition of function. After increasing, number of candidates become (140% of 4k), (160% of 5k) & (185% ... 111k/10 Now, the required new ratio is: 56k/100 : 80k/10 : 111k/10 = 56 : 80 : 111, A ................. complete subgraph and a ................. subset of vertices of a graph G=(V,E) are a clique and a vertex cover respectively. i.e. Then f(Around - 4) is given by: (A) {(2,0.6), (3,0.3), (6,1), (11,0.3)} (B) {(2,0.6), (3,1), (6,1), (11,0.3)} (C) {(2,0.6), (3,1), (6,0.6), (11,0.3)} (D) {(2,0.6), (3,0.3), (6,0.6), (11,0.3)}, Consider the reference string 0 1 2 3 0 1 4 0 1 2 3 4 If FIFO page replacement algorithm is used, then the number of page faults with three page frames and four page frames are .......... and ........... respectively. if an empty frame is available or if the replaced page is not modified, and it takes 20 m.secs., if the replaced page is modified. (2) Compiler does not set up a separate function for every definition of function.  = {16×15×14×13×12×11×10×9×8×7×6×5×4×3×2 } /  {(10×9×8×7×6×5×4×3×2 ) (2) (4×3×2)}}  = {16×15×14×13×12×11} / {(2)(4×3×2)}  = {8×5×7×13×3×11}  = 120120, A Multicomputer with 256 CPUs is organized as 16x16 grid. Correct sum of these 8 articles = (incorrect sum) - (sum of incorrect articles) + (sum of actual articles) = [120 ... (30)] = 130 Therefore, correct mean = 130/8 = 16.25 Hence, the correct mean is 16.25. How to solve: Prove that a complete graph (a graph in which there is an edge between every pair of vertices) has n^(n-2) spanning trees. A) 25230 B) 23420 C) 120120 D) 27720, Answer: C)  Number of different arrangements possible  = {16!} In a demand paging memory system, page table is held in registers. (a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree. For any complete graph K n with n nodes, different spanning trees possible is n (n-2) So, spanning trees in complete graph K4 will be 4 (4 - 2). Inorder Tree Traversal without recursion and without stack! Hence we can compute co-factor for any element of the matrix. Suppose the function y and a fuzzy integer number around -4 for x are given as y=(x-3)2+2 Around -4={(2,0.3), (3,0.6), (4,1), (5,0.6), (6,0.3)} respectively. Here we’ve constructed four spanning trees from the graph . ................ is used in game trees to reduce the number of branches of the search tree to be traversed without affecting the solution. The number of edges in this graph is (A) 726 (B) 796 (C) 506 (D) 616, The language of all non-null strings of a’s can be defined by a context free grammar as follow : S→a S|S a| a The word a3 can be generated by ................ different trees. How many days will they now take to complete the remaining work? Counting the trees of K The number of labelled spanning trees of the complete graph Kwas given by Cayley [2] in 1889 by the formula IT(n)~ =n"-2. (A) 4 (B) 3 (C) 2 (D) 1, Given two sorted list of size 'm' and 'n' respectively. (B) Shift step that advances in the input stream by one symbol and Reduce step that applies a completed grammar rule to some recent parse trees, joining them together as one tree with a new root symbol. Find the number of hours taken by pipe R to fill the tank if the remaining tank is filled in 14 hours. A) 16 B) 14 C) 20 D) 42, D 1/P + 1/Q + 1/R = 1/12 Now given that first all open for 2hours, then R closed and P+Q completes in 14 hours, so (1/P + 1/Q + 1/R) *2 + (1/P + 1/Q)*14 = 1 Put 1/P + 1/Q = 1/12 – 1/R (1/12 – 1/R + 1/R) *2 + (1/12 – 1/R)*14 = 1 1/6+ 14/12 – 14/R = 1 Solve, R = 42, There are 10 orange, 2 violet and 4 purple balls in a bag. Every neighborly polytope in four or more dimensions also has a … Counting spanning trees The number t(G) of spanning trees of a connected graph is a well-studied invariant. In complete graph, the task is equal to counting different labeled trees with n nodes for which have Cayley’s formula. (A) SSTF (shortest seek time first) algorithm increases performance of FCFS. Yes. (D) 14 m.sec. (A) 5 (B) n – 3 (C) 20 (D) 11. (b) A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree. The total number of head movements using Shortest Seek Time First (SSTF) and SCAN algorithms are respectively (A) 236 and 252 cylinders (B) 640 and 236 cylinders (C) 235 and 640 cylinders (D) 235 and 252 cylinders, Consider the graph given below: The two distinct sets of vertices, which make the graph bipartite are: (A) (v1, v4, v6); (v2, v3, v5, v7, v8) (B) (v1, v7, v8); (v2, v3, v5, v6) (C) (v1, v4, v6, v7); (v2, v3, v5, v8) (D) (v1, v4, v6, v7, v8); (v2, v3, v5), Consider a program that consists of 8 pages (from 0 to 7) and we have 4 page frames in the physical memory for the pages. STEP 2: Replace all the diagonal elements with the degree of nodes. if an empty frame is available or if the replaced page is not modified, and it takes 20 m.secs., if the replaced page is modified. 2. to manage changes to one or more of these items. (A) Software Quality Management Process (B) Software Configuration Management Process (C) Software Version Management Process (D) Software Change Management Process, Assuming that the disk head is located initially at 32, find the number of disk moves required with FCFS if the disk queue of I/O block requests are 98, 37, 14, 124, 65, 67: (A) 310 (B) 324 (C) 320 (D) 321, Suppose that we have numbers between 1 and 1000 in a binary search tree and want to search for the number 364. On rechecking, it was found that two article were wrongly taken as 11 and 9 instead of 16 and 14 respectively. The number of different spanning trees in complete graph, K4 and bipartite graph K2,2 have ..... and ..... . Shift-Reduce parsers perform the following : (A) Shift step that advances in the input stream by K(K>1) symbols and Reduce step that applies a completed grammar rule to some recent parse trees, joining them together as one tree with a new root symbol. 0 Lemma 2. D) Calculated mean of 8 articles = 15 Incorrect sum of these 8 articles = (15*8) = 120. Which one of the following is used to compute cyclomatic complexity ? 3. to facilitate the construction of different versions of an application. (A) 11.6 m.sec. A graph can have many spanning trees. The number of days taken by vikram to do the same piece of work. A complete undirected graph can have maximum nn-2 number of spanning trees, where n is the number of nodes. The number of different spanning trees in complete graph, K4 and bipartite graph K2,2 have .......... and .....…. They are as follows − These three are the spanning trees for the given graphs. How many cliques are there in the graph shown below? discussed, as well as how it can be used to enumerate the spanning trees of a complete graph and a complete bipartite graph.

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