The Generalized Competition Indices of Doubly Symmetric Primitive Digraphs with d Loops

Let DSn(d) denote the set of all doubly symmetric primitive digraphs of order n with d loops, where d is an integer and 1 <= d <= n. In this paper, we determine the upper bounds for the m-competition indices(generalized competition indices) of DSn(d), where 1 <= m <= n. If n and d satisfy that n is odd and d is odd, or n <= 2d-2 and d is even such that d >= 2, then the upper bounds for the m-competition indices of DSn(d) can be reached, where 1 <= m <= n.

Automated summary

In this paper, we determine the upper bounds for the m-competition indices of doubly symmetric primitive digraphs DSn(d), and show that these bounds can be reached under certain conditions.