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Ars Combinatoria

  • Research article

The Extremal Primitive Digraph with Both Lewin Index \(n – 2\) and Girth \(2\) or \(3\)

Guanglong Yu1,2, Zhengke Miao3, Chao Yan4, Jinlong Shu2
1Department of Mathematics, Yancheng Teachers University, Yancheng, 224002, P.R. China
2Department of Mathematics, East China Normal University, Shanghai, 200241, P.R. China
3Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, China
4Department of Mathematics and Phisics, University of science and Technology, PLA Nanjing, 211101, P.R. China
  • Published: 31/07/2014

Abstract

Let \(D\) be a primitive digraph. Then there exists a nonnegative integer \(k\) such that there are walks of length \(k\) and \(k+1\) from \(u$ to \(v\) for some \(u,v \in V(D)\) (possibly \(u\) again ). Such smallest \(k\) is called the Lewin index of the digraph \(D\), denoted by \(l(D)\). In this paper, the extremal primitive digraphs with both Lewin index \(n — 2\) and girth \(2\) or \(3\) are determined.

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Citation
Guanglong Yu, Zhengke Miao, Chao Yan, Jinlong Shu. The Extremal Primitive Digraph with Both Lewin Index \(n – 2\) and Girth \(2\) or \(3\)[J], Ars Combinatoria, Volume 115. 401-410. .