Journal
SYMMETRY-BASEL
Volume 14, Issue 6, Pages -Publisher
MDPI
DOI: 10.3390/sym14061192
Keywords
symmetric digraph; m-competition index; generalized competition index; competition index; scrambling index
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Funding
- Shanghai Institute of Technology [10120K226052-A06]
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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.
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.
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