Unicyclic graphs with regular endomorphism monoids-Reference-Cited by-同舟云学术

Unicyclic graphs with regular endomorphism monoids

Published:2016-05-26 Issue:02 Volume:08 Page:1650020
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Ma Xiaobin¹,Wong Dein²,Zhou Jinming²

Affiliation:

1. School of Science, Anhui University of Science and Technology, Huainan, 232001, People’s Republic of China

2. Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China

Abstract

The motivation of this paper comes from an open question: which graphs have regular endomorphism monoids? In this paper, we give a definitely answer for unicyclic graphs, proving that a unicyclic graph [Formula: see text] is End-regular if and only if, either [Formula: see text] is an even cycle with 4, 6 or 8 vertices, or [Formula: see text] contains an odd cycle [Formula: see text] such that the distance of any vertex to [Formula: see text] is at most 1, i.e., [Formula: see text]. The join of two unicyclic graphs with a regular endomorphism monoid is explicitly described.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830916500208

Reference22 articles.

1. Endomorphism spectra of graphs

2. On End-regular graphs

3. End-Regularity of the Join of n Split Graphs

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