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### ON EXPONENTS OF PRIMITIVE GRAPHS

#### Abstract

A connected gaph 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

t that connects u and v. The smallest of such positive integers k is called

the exponent of G and is denoted by exp(G). In this paper, we give a new

bound on exponent of primitive graphs G in terms of the length of the

smallest cycle of G. We show that the new bound is sharp and

generalizes the bounds given by Shao and Liu et. al.

Keywords: primitive graphs; exponents.

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