Abstract
For a primitive digraph D of order n and a positive integer m such that m≤n, the m-competition index of D is defined as the smallest positive integer k such that for every pair of vertices x and y, there exist m distinct vertices v1,v2,…,vm such that there are directed walks of length k from x to vi and from y to vi for 1≤i≤m in D. In this study, we investigate m-competition indices of symmetric primitive digraphs and provide the upper and lower bounds. We also characterize the set of m-competition indices of symmetric primitive digraphs.
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