On the Turán Number of Km ∨ C2k-1

Given a graph H and a positive integer n, the Tur & aacute;n number of H of the order n, denoted by ex(n, H), is the maximum size of a simple graph of order n that does not contain H as a subgraph. Given graphs G and H, G boolean OR H denotes the join of G and H. In this paper, we prove ex(n, K-m boolean OR C2k-1) = [ (m+1)n(2)/2(m+2) ] for n >= 2(m + 2)k - 3(m + 2) - 1.