The generalized competition indices of primitive minimally strong digraphs

Wei Fang, Yubin Gao, Yanling Shao, Wei Gao, Guangming Jing, Zhongshan Li

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Let D be a primitive digraph of order n and 1≤m≤n. The m-competition index of D is the smallest positive integer k such that every pair of vertices x and y of D have at least m common preys in Dk. In this paper, the upper bound of m-competition indices (1≤m≤n-1) for primitive minimally strong digraphs of order n is obtained. Furthermore, it is shown that for 1≤m≤n-1, there exist "gaps" in the m-competition index set of primitive minimally strong digraphs of order n.

Original languageEnglish (US)
Pages (from-to)206-226
Number of pages21
JournalLinear Algebra and Its Applications
Volume493
DOIs
StatePublished - Mar 15 2016
Externally publishedYes

Keywords

  • Minimally strong digraph
  • Primitive digraph
  • m-competition index

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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