Scrambling index of certain primitive graphs consisting of two disjoint odd cycles connected by some paths

Abstract

The scrambling index of a primitive graph G is the smallest positive integer k such that for each pair of vertices u and v there is a vertex w such that there exists a uw-walk and a vw-walk of length k. We discuss the scrambling index of primitive graphs G consisting of two disjoint odd cycles each of length s connected by some paths of length ℓ0. For such primitive graphs G we present formulae for scrambling indices that depend on s and ℓ0.