# IJPAM: Volume 119, No. 1 (2018)

# Title

CHARACTERIZATIONS FOR PRINCIPALIDEAL GRAPHS OF RECTANGULAR GROUPS

# Authors

John MeksawangFaculty of Science

Nakhon Phanom University

Nakhon Phanom, THAILAND

# Abstract

A principal right ideal graph of a semigroup is the graph whose vertex set is and any two vertices and () are adjacent if and only if . We denote the principal right ideal graph of a semigroup by . A principal left ideal graph of a semigroup is defined dually and is denoted by . We define a principal ideal graph of a semigroup as the graph with is the vertex set and any two vertices and () are adjacent in if and only if and . 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**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2018

**Volume:**119

**Issue:**1

**Pages:**249 - 259

Google Scholar; DOI (International DOI Foundation); WorldCAT.

**This work is licensed under the Creative Commons Attribution International License (CC BY).**