# 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 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

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

## Bibliography

1
S. Akbari, M. Ghandehari, M. Hadian and A. Mohammadian, On commuting graphs of semisimple rings, Linear Algebra Appl., 390, (2004), 345-355.

2
S. Akbari, A. Mohammadian, H. Radjavi and P. Raja, On the diameters of commuting graphs, Linear Algebra Appl., 418, 1(2006), 161-176.

3
B. Csakany and G. Pollak, The graph of subgroups of a finite group, Czechoslovak Math. J., 19, (1969), 241-247.

4
R.S. Indu and L. John, Principal Ideal Graphs of Rectangular Bands, Mathematical Theory and Modeling, 9, 2(2012), 59-68.

5
A. V. Kelarev and C. E. Praeger, On Transitive Cayley Graphs of Groups and Semigroups, European Journal of Combinatorics, 24, (2003), 59-72.

6
B. Khosravi and M. Mahmoudi, On Cayley graphs of rectangular groups, Discrete Mathematics, 310, (2010), 804-811.

7
S. Panma, U. Knauer, N. Na Chiangmai and Sr. Arworn, Characterization of Clifford Semigroup Digraphs, Discrete Mathematics, 306, (2006), 1247-1252.

8
S. Panma and J. Meksawang, Isomorphism Conditions for Cayley Graphs of Rectangular Groups, Bull. Malays. Math. Sci. Soc., 39, (2016), 29-41.

9
A. Rosenfeld, Fuzzy graphs, in: L.A. Zadeh, K.S. Fu and M. Shimura (Eds), Fuzzy Sets and their Applications, Academic Press, New York(1975).

# 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