. Consider a network with M edges. Let k denote the number of bridges in the network

Chapter 7, Problem 44

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QUESTION:

. Consider a network with M edges. Let k denote the number of bridges in the network. (a) If M = 5, list all the possible values of k. (b) If M = 123, describe the set of all possible values of k.

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QUESTION:

. Consider a network with M edges. Let k denote the number of bridges in the network. (a) If M = 5, list all the possible values of k. (b) If M = 123, describe the set of all possible values of k.

ANSWER:

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(a) We are given the number of edges are , this network can either be a tree where all edges are bridges and hence , or it can a simple network, and a simple network must have at least one circuit, and there cannot be a circuit of length one or two. Meaning that  cannot have the values of

therefore, the possible values of  are

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