Shahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901THE UNIT GRAPH OF A COMMUTATIVE SEMIRING7989283610.22044/jas.2022.11957.1612ENLaithun BoroDepartment of Mathematics, North-Eastern Hill University P.O. Box 793022,
Shillong, India.0000-0002-3852-1755Madan MohanSinghDepartment of Basic Sciences & Social Sciences, North-Eastern Hill University,
P.O. Box 793022, Shillong, India.0000-0002-1088-6832Jituparna GoswamiDepartment of Mathematics, Gauhati University, P.O. Box 781014, Guwahati,
India.0000-0002-1786-752XJournal Article20220531Let 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.https://jas.shahroodut.ac.ir/article_2836_cf33c9288a9bbc12414f964d9bc4eb79.pdf