EXPONENTS OF PRIMITIVE GRAPHS CONTAINING TWO DISJOINT ODD CYCLES - Indra Syahputra (Proceedings of ICMSA, 2006)
A connected graph G is primitive provided there exists a positive integer k such that for each pair of vertices u and v in G there is a walk of length k connecting u and v. The smallest of such positive integer k is the exponent of G. A primitive graph is said to be odd primitive graph if it has an odd exponent. It is known that if G is an odd primitive graph then G contains two disjoint odd cycles. This paper discusses exponents of a class of primitivegraphs containing of exactly two disjoint odd cycles. For such graphs we characterize the odd and even primitive graphs.