N. Pipattanajinda, U. Knauer, B. Gyurov, S. Panma, “The endomorphism monoids of ($n-3$)-regular graphs of order $n$”, Algebra Discrete Math., 2016, Volume 22, Issue 2,Pages 284

This article is cited in 4 papers

RESEARCH ARTICLE

The endomorphism monoids of ($n-3$)-regular graphs of order $n$

N. Pipattanajinda^a, U. Knauer^b, B. Gyurov^c, S. Panma^d

^a Program of Mathematics, Faculty of Science and Technology, Kamphaeng Phet Rajabhat University, Kamphaeng Phet 62000, THAILAND
^b Institut für Mathematik, Carl von Ossietzky Universität, D-26111 Oldenburg, GERMANY
^c School of Science and Technology, Georgia Gwinnett College, University System of Georgia, Lawrenceville, GA 30043, USA
^d Department of Mathematics, Faculty of Sciences, Chiang ai University, Chiang Mai 50200, THAILAND

Abstract: This paper is motivated by the result of W. Li, that presents an infinite family of graphs - complements of cycles — which possess a regular monoid. We show that these regular monoids are completely regular. Furthermore, we characterize the regular, orthodox and completely regular endomorphisms of the join of complements of cycles, i.e. ($n-3$)-regular graphs of order $n$.

Keywords: complement of cycle, join, endomorphism monoid, completely regular, orthodox.

MSC: 05C25, 05C38

Received: 16.03.2012
Revised: 03.03.2015

Language: English