THE UNIT GRAPH OF A COMMUTATIVE SEMIRING

Document Type : Original Manuscript

Authors

1 Department of Mathematics, North-Eastern Hill University P.O. Box 793022, Shillong, India.

2 Department of Basic Sciences & Social Sciences, North-Eastern Hill University, P.O. Box 793022, Shillong, India.

3 Department of Mathematics, Gauhati University, P.O. Box 781014, Guwahati, India.

Abstract

Let S be a commutative semiring with unity and U(S) be the set of all units of S. The unit graph of S, denoted by G(S), is the undirected graph with vertex set S and two distinct vertices x and y are adjacent if and only if x + y ∈ U(S). In this article, we have investigated some properties of unit graph G(S) of S regarding completeness, bipartiteness, connectedness, diameter and girth. Finally, we find a necessary and sufficient condition for G(S) to be traversable.

Keywords

References

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Journal of Algebraic Systems
Volume 12, Issue 1
September 2024
Pages 79-89

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