Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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LINE GRAPHS OF UNIT GRAPHS ASSOCIATED WITH THE DIRECT PRODUCT OF RINGS

  • Pirzada, S. (Department of Mathematics, University of Kashmir) ;
  • Altaf, Aaqib (Department of Mathematics, University of Kashmir)
  • Received : 2021.05.31
  • Accepted : 2022.01.04
  • Published : 2022.03.30
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Abstract

Let R be a finite commutative ring with non zero identity. The unit graph of R denoted by G(R) is the graph obtained by setting all the elements of R to be the vertices of a graph and two distinct vertices x and y are adjacent if and only if x + y ∈ U(R), where U(R) denotes the set of units of R. In this paper, we find the commutative rings R for which G(R) is a line graph. Also, we find the rings for which the complements of unit graphs are line graphs.

Keywords

Acknowledgement

We are grateful to the anonymous referees for their valuable suggestions which improved the presentation.

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