IJPAM: Volume 119, No. 1 (2018)

Title

CHARACTERIZATIONS FOR PRINCIPAL
IDEAL GRAPHS OF RECTANGULAR GROUPS

Authors

John Meksawang
Faculty of Science
Nakhon Phanom University
Nakhon Phanom, THAILAND

Abstract

A principal right ideal graph of a semigroup $S$ is the graph whose vertex set is $S$ and any two vertices $x$ and $y$ ($x\neq y$) are adjacent if and only if $xS \cap yS \neq \emptyset$. We denote the principal right ideal graph of a semigroup $S$ by $\Gamma_S$. A principal left ideal graph of a semigroup $S$ is defined dually and is denoted by $_S\Gamma$. We define a principal ideal graph of a semigroup $S$ as the graph $_S\Gamma_S$ with $S$ is the vertex set and any two vertices $x$ and $y$ ($x\neq y$) are adjacent in $_S\Gamma_S$ if and only if $Sx \cap Sy \neq \emptyset$ and $xS \cap yS \neq \emptyset$. A rectangular band is defined as a direct product of a left zero semigroup and a right zero semigroup. A rectangular group is defined as a direct product of a group and a rectangular band. The principal ideal graph of a rectangular group is studied in this paper. First, we characterize the principal right ideal graphs and the principal left ideal graphs of a rectangular groups. Finally we characterize the principal ideal graphs of a rectangular groups.

History

Received: May 26, 2017
Revised: June 13, 2018
Published: June 20, 2018

AMS Classification, Key Words

AMS Subject Classification: 05C25, 08B15, 20M19, 20M30
Key Words and Phrases: rectangular groups, principal ideal graphs, connected graphs, complete graphs

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How to Cite?

DOI: 10.12732/ijpam.v119i1.20 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 1
Pages: 249 - 259


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