IJPAM: Volume 119, No. 1 (2018)
IDEAL GRAPHS OF RECTANGULAR GROUPS
Faculty of Science
Nakhon Phanom University
Nakhon Phanom, THAILAND
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.
Received: May 26, 2017
Revised: June 13, 2018
Published: June 20, 2018
AMS Subject Classification: 05C25, 08B15, 20M19, 20M30
Key Words and Phrases: rectangular groups, principal ideal graphs, connected graphs, complete graphs
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 249 - 259