The Maximum Possible Number of Edges in a Simple Graph with at Most Two Cycles Having the Same Length
Shi Yong-bing · 2003
Let Sn be the set of simple graphs on n vertices in which at most two cycles have the same length. A graph C is said to be a simple maximum cycle distributed(2) graph (Simple MCD(2)-graph) if there does not exist a graph G1 in Sn such that I E( G') | | E( G)| . Let f (n,2) be the number of edges in a simple MCD(2) - graph on n vertices. In this paper , we prove that f(n,2) (n - 1) + [1/2,11n -20]for each integer n 3 , and the equality holds when