0 votes 0 votes Which two of the following are equivalent for an undirected graph G ? (i) G is a tree (ii) There is at least one path between any two distinct vertices of G (iii) G contains no cycles and has (n-1) edges (iv) G has n edges (i) and (ii) (i) and (iii) (i) and (iv) (ii) and (iii) Graph Theory ugcnetcse-june2009-paper2 + – rishu_darkshadow asked Sep 22, 2017 • edited Jun 23, 2020 by soujanyareddy13 rishu_darkshadow 4.7k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes A connected acyclic graph is called a tree. Tree is connected (there is a path between any two distinct vertices) and has n-1 edges because of zero cycles and connectedness. Answer B Shivam Chauhan answered Sep 22, 2017 Shivam Chauhan comment Share Follow See all 2 Comments See all 2 2 Comments reply rishu_darkshadow commented Sep 26, 2017 reply Follow Share @ Shivam Chauhan but they said "undirected graph"....how you consider it as a acyclic graph ? 0 votes 0 votes Shivam Chauhan commented Sep 26, 2017 reply Follow Share They asked which two statements are equivalent to each other if G is undirected graph. Suppose I take (i) statement as true then (iii) must also be true because tree has zero cycles (acyclic) and n-1 edges Consider your answer (ii) statement to be true then it implies only G is connected not about the number of edges so (iv) may or may not be true 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Default graph is simple, undirected graph.. For simple graph, it has no self loop and parallel edges Ans: D rishu_darkshadow answered Sep 26, 2017 rishu_darkshadow comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Answer is D; As default graph is a simple graph & it is undirected and it has no self loop and parallel edges divya sree 1 answered Sep 26, 2017 divya sree 1 comment Share Follow See all 0 reply Please log in or register to add a comment.