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The number of edges in a regular graph of degree 46 and 8 vertices is ____________

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The number of edges in a regular graph of degree 46 and 8 vertices is ____________

(a) 347

(b) 230

(c) 184

(d) 186

This question was addressed to me in semester exam.

This key question is from Graphs Properties in division Graphs of Discrete Mathematics

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Correct choice is (c) 184

Explanation: In a complete graph which is (n-1) regular (where n is the number of vertices) has edges n*(n-1)/2. In the graph n vertices are adjacent to n-1 vertices and an edge contributes two degree so dividing by 2. Hence, in a d regular graph number of edges will be n*d/2 = 46*8/2 = 184.

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