Algorithms
Q131.
The graph shown below has 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 and contains the edges: {(A, C), (B, C), (B, E), (E, F), (D, F)}. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all 8 edges of this graph is ___________.Q132.
Let s and t be two vertices in a undirected graph G=(V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s\inX and t\inY. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. The edge e must definitely belong to:Q133.
An undirected graph G has n nodes. Its adjacency matrix is given by an nxn square matrix whose (i) diagonal elements are 0's and (ii) non-diagonal elements are 1's. which one of the following is TRUE?Q134.
Let s and t be two vertices in a undirected graph G=(V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s\inX and t\inY. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?Q135.
An undirected graph G(V, E) contains n (n>2) nodes named v1 , v2 ,...,vn. Two nodes vi , vj are connected if and only if 0\lt |i-j|\leq2. Each edge (vi,vj ) is assigned a weight i+j. A sample graph with n=4 is shown below. The length of the path from v5 to v6 in the MST of previous question with n = 10 isQ136.
Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:Kruskal's algorithm for finding a minimum spanning tree of a weighted graph G with n vertices and m edges has the time complexity of:Q137.
G = (V,E) is an undirected simple graph in which each edge has a distinct weight,and e is a particular edgeof G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE? I. If e is the lightest edge of some cycle in G, then every MST of G includes e II. If e is the heaviest edge of some cycle in G, then every MST of G excludes eQ139.
What is the largest integer m such that every simple connected graph with n vertices and n edges contains at least m different spanning trees ?Q140.
Let G be a connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.