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ON EXPONENTS OF PRIMITIVE GRAPHS

Saib Suwilo

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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