### EXPONENTS OF PRIMITIVE GRAPHS CONTAINING TWO DISJOINT ODD CYCLES

#### Abstract

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 primitive

graphs containing of exactly two disjoint odd cycles. For such graphs we characterize the odd and even primitive graphs.

graphs containing of exactly two disjoint odd cycles. For such graphs we characterize the odd and even primitive graphs.

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