Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths

Zejun Huang; Xingzhi Zhan

doi:10.1016/j.disc.2012.04.008

Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths

Zejun Huang
, Xingzhi Zhan^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Let D be a digraph of order n in which any two walks with the same initial vertex and the same terminal vertex have distinct lengths. We prove that D has at most ( ⁿ⁺¹⁾²4 arcs if n is odd and n(n+2)4 arcs if n is even. The digraphs attaining this maximum size are determined.

Original language	English
Pages (from-to)	2203-2213
Number of pages	11
Journal	Discrete Mathematics
Volume	312
Issue number	15
DOIs	https://doi.org/10.1016/j.disc.2012.04.008
State	Published - 6 Aug 2012

Keywords

0-1 matrix
Digraph
Extremal digraph
Walk

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10.1016/j.disc.2012.04.008

Cite this

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title = "Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths",

abstract = "Let D be a digraph of order n in which any two walks with the same initial vertex and the same terminal vertex have distinct lengths. We prove that D has at most ( n+1)24 arcs if n is odd and n(n+2)4 arcs if n is even. The digraphs attaining this maximum size are determined.",

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author = "Zejun Huang and Xingzhi Zhan",

year = "2012",

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doi = "10.1016/j.disc.2012.04.008",

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T1 - Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths

AU - Huang, Zejun

AU - Zhan, Xingzhi

PY - 2012/8/6

Y1 - 2012/8/6

N2 - Let D be a digraph of order n in which any two walks with the same initial vertex and the same terminal vertex have distinct lengths. We prove that D has at most ( n+1)24 arcs if n is odd and n(n+2)4 arcs if n is even. The digraphs attaining this maximum size are determined.

AB - Let D be a digraph of order n in which any two walks with the same initial vertex and the same terminal vertex have distinct lengths. We prove that D has at most ( n+1)24 arcs if n is odd and n(n+2)4 arcs if n is even. The digraphs attaining this maximum size are determined.

KW - 0-1 matrix

KW - Digraph

KW - Extremal digraph

KW - Walk

UR - https://www.scopus.com/pages/publications/84860652390

U2 - 10.1016/j.disc.2012.04.008

DO - 10.1016/j.disc.2012.04.008

M3 - 文章

AN - SCOPUS:84860652390

SN - 0012-365X

VL - 312

SP - 2203

EP - 2213

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 15

ER -

Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths

Abstract

Keywords

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