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An n-vertex graph has ______ edges.(a) n^2(b) n-1(c) n*n(d) n*(n+1)/2This question was addressed to me in exam.I would like to ask this question from Properties of Tree topic in chapter Trees of Discrete Mathematics

Answer»

Correct answer is (b) n-1

For explanation I would SAY: Suppose G is a connected graph which has no cycles. Every subgraph of G INCLUDES at least one VERTEX with zero or one incident edges. It has n vertices and n-1 edges. Generally, the order-zero graph is not considered to be a tree.



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