The generalized competition indices of primitive minimally strong digraphs

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

doi:10.1016/j.laa.2015.11.036

The generalized competition indices of primitive minimally strong digraphs

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

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5 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 language	English (US)
Pages (from-to)	206-226
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	493
DOIs	https://doi.org/10.1016/j.laa.2015.11.036
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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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.",

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author = "Wei Fang and Yubin Gao and Yanling Shao and Wei Gao and Guangming Jing and Zhongshan Li",

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doi = "10.1016/j.laa.2015.11.036",

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T1 - The generalized competition indices of primitive minimally strong digraphs

AU - Fang, Wei

AU - Gao, Yubin

AU - Shao, Yanling

AU - Gao, Wei

AU - Jing, Guangming

AU - Li, Zhongshan

PY - 2016/3/15

Y1 - 2016/3/15

N2 - 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.

AB - 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.

KW - Minimally strong digraph

KW - Primitive digraph

KW - m-competition index

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DO - 10.1016/j.laa.2015.11.036

M3 - Article

AN - SCOPUS:84951020419

SN - 0024-3795

VL - 493

SP - 206

EP - 226

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The generalized competition indices of primitive minimally strong digraphs

Abstract

Keywords

ASJC Scopus subject areas

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