Prove that G G when G is a graph with girth 5 and diameter

Prove that (G) = (G) when G is a graph with girth 5 and diameter 2.

Solution

the graph has a girth 5 . So the smallest cycle is 5-cycle

diameter 2 means maximum distance between any pair of vertices is 2 .

This means graph is a a cycle of length 5.( the only possible graph)

=> k(G) = delta(G) = 2