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Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive any distinct. Consider the following statements: -gate computer science 20171 AnswerLet G be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE? P: Minimum spanning tree of G does not change Q: Shortest pat1 AnswerThe graph shown below 8 edges with distinct integer edge weights. -gate-cse-20151 AnswerLet w be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight w. Which of the following is FALSE?-computer science-gate-2007 1 AnswerLet G be a weighted graph with edge weights greater than one and Gbe the graph constructed by squaring the weights of edges in G. Let T and T be the minimum spanning trees of G and G, respectively, with total weights t and t. Which of the following i1 AnswerLet G be an undirected connected graph with distinct edge weight. GATE CSE 20001 AnswerLet G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to A -gate-cse-20121 Answerhow to find the number of bounded faces in an undirected graph?1 AnswerLet G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2, 3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can have is ____. Gate-cs-20161 AnswerLet G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree GATE CSE 20001 AnswerLet G be a simple undirected planar graph on 10 vertices with 15edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to -gate-computer science-20121 AnswerLet G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to -gate-computer science-20121 AnswerLet G be the non-planar graph with the minimum possible number of edges. Then G has -computer science-gate-20071 AnswerConsider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three? -gate-computer science-20121 AnswerWhich of the following statements are TRUE? -gate-computer science-20131 AnswerIn an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity, by -computer science-gate-20071 Answer Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is _______________.-gate-cse-20151 AnswerA positive edge-triggered D flip-flop is connected to a positive edge-triggered JK flipflop as follows. -gate-cse-20151 AnswerLet G = (V, E) be a simple undirected graph, and s be a particular vertex in it called the source. -gate-cse-20151 AnswerLet G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to -gate-cse-20121 Answer