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

Abstract

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.