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- Title
Upper Bounds of the Generalized Competition Indices of Symmetric Primitive Digraphs with d Loops.
- Authors
Chen, Danmei
- Abstract
A digraph (D) is symmetric if (u , v) is an arc of D and if (v , u) is also an arc of D. If a symmetric digraph is primitive and contains d loops, then it is said to be a symmetric primitive digraph with d loops. The m-competition index (generalized competition index) of a digraph is an extension of the exponent and the scrambling index. The m-competition index has been applied to memoryless communication systems in recent years. In this article, we assume that S n (d) represents the set of all symmetric primitive digraphs of n vertices with d loops, where 1 ≤ d ≤ n. We study the m-competition indices of S n (d) and give their upper bounds, where 1 ≤ m ≤ n. Furthermore, for any integer m satisfying 1 ≤ m ≤ n , we find that the upper bounds of the m-competition indices of S n (d) can be reached.
- Subjects
MEMORYLESS systems; TELECOMMUNICATION systems
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 7, p1348
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15071348