Generalized competition indices of symmetric primitive digraphs

For a primitive digraph DD of order nn and a positive integer mm such that m≤nm≤n, the mm-competition index of DD is defined as the smallest positive integer kk such that for every pair of vertices xx and yy, there exist mm distinct vertices v1,v2,…,vmv1,v2,…,vm such that there are directed walks of length kk from xx to vivi and from yy to vivi for 1≤i≤m1≤i≤m in DD. In this study, we investigate mm-competition indices of symmetric primitive digraphs and provide the upper and lower bounds. We also characterize the set of mm-competition indices of symmetric primitive digraphs.