Data Structures Algorithms-II MCQs

Page No. 64

hich of the following is false?


aThe spanning trees do not have any cycles


bMST have n – 1 edges if the graph has n edges


cEdge e belonging to a cut of the graph if has the weight smaller than any other edge in the same cut, then the edge e is present in all the MSTs of the graph


dRemoving one edge from the spanning tree will not make the graph disconnected



Which of the following is not the algorithm to find the minimum spanning tree of the given graph?


aBoruvka’s algorithm


bPrim’s algorithm


cKruskal’s algorithm


dBellman–Ford algorithm



If all the weights of the graph are positive, then the minimum spanning tree of the graph is a minimum cost subgraph.


a True


bFalse


ceither A. or B.


d None of these


View Answer True

Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?


aEvery minimum spanning tree of G must contain CD


b If AB is in a minimum spanning tree, then its removal must disconnect G


cNo minimum spanning tree contains AB


dG has a unique minimum spanning tree



The travelling salesman problem can be solved using _________


aA spanning tree


bA minimum spanning tree


cBellman – Ford algorithm


dDFS traversal



Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.


a15


b8


c16


d13


View Answer 16

Every graph has only one minimum spanning tree.


aTrue


bFalse


ceither A. or B.


d None of these


View Answer False

Which of the following is false in the case of a spanning tree of a graph G?


aIt is tree that spans G


bIt is a subgraph of the G


cIt includes every vertex of the G


d It can be either cyclic or acyclic



Consider the following statements.
S1. Kruskal’s algorithm might produce a non-minimal spanning tree.
S2. Kruskal’s algorithm can efficiently implemented using the disjoint-set data structure.


aS1 is true but S2 is false


bBoth S1 and S2 are false


cBoth S1 and S2 are true


dS2 is true but S1 is false



Kruskal’s algorithm is best suited for the dense graphs than the prim’s algorithm.


aTrue


bFalse


ceither A. or B.


d None of these


View Answer True

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