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On Another Class of Strongly Perfect Graphs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Neha Kansal & Bableen Kaur & Pravin Garg & Deepa Sinha, 2022. "On Another Class of Strongly Perfect Graphs," Mathematics, MDPI, vol. 10(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2014-:d:836498
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