On Another Class of Strongly Perfect Graphs

Neha Kansal, Bableen Kaur, Pravin Garg and Deepa Sinha
Additional contact information
Neha Kansal: Department of Mathematics, University of Rajasthan, Jaipur 302004, India
Bableen Kaur: Department of Mathematics, South Asian University, New Delhi 110021, India
Pravin Garg: Department of Mathematics, University of Rajasthan, Jaipur 302004, India
Deepa Sinha: Department of Mathematics, South Asian University, New Delhi 110021, India

Mathematics, 2022, vol. 10, issue 12, 1-20

Abstract: For a commutative ring R with unity, the associate ring graph, denoted by A G ( R ) , is a simple graph with vertices as nonzero elements of R and two distinct vertices are adjacent if they are associates. The graph A G ( R ) contains components equal in number to the number of distinct orbits, except for the orbit of an element 0. Moreover, each component is a complete graph. An important finding is that this is a class of strongly perfect graphs. In this article we describe the structure of the associate ring graph of the ring of integers modulo n , denoted by A G ( Z n ) . We carried out computer experiments and provide a program for the same. We further characterize cases in which A G ( Z n ) , its complement A G ( Z n ) ¯ , and their line graphs are planar, ring graphs, and outerplanar. We also discuss the properties of the associate ring graph of a commutative ring R with unity.

Keywords: associate ring graph; ring graph; line graph; planar; outerplanar (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/12/2014/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/12/2014/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:12:p:2014-:d:836498

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().