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G be a connected graph with n vertices and m edges

G be a connected graph with n vertices and m edges

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Let G be a connected graph with n vertices and m edges.
Which of the following statements are true?
(i) G is a tree if and only if n = m+1.
(ii) G is a tree if and only if m = n+1.
(iii) G is a tree if and only if the addition of any edge
to G will produce a unique cycle.
(iv) G is a tree if and only if G contains at least one
path b etween any two vertices.
(v) If G is connected, then G is a tree if and only if G
contains at most one path between any two vertices.
(vi) A connected subgraph of a tree is always a tree.

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