### 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 language | English (US) |
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Pages (from-to) | 206-226 |

Number of pages | 21 |

Journal | Linear Algebra and Its Applications |

Volume | 493 |

DOIs | |

State | Published - Mar 15 2016 |

Externally published | Yes |

### 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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## Cite this

Fang, W., Gao, Y., Shao, Y., Gao, W., Jing, G., & Li, Z. (2016). The generalized competition indices of primitive minimally strong digraphs.

*Linear Algebra and Its Applications*,*493*, 206-226. https://doi.org/10.1016/j.laa.2015.11.036