%0 Journal Article
%T THE UNIT GRAPH OF A COMMUTATIVE SEMIRING
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Boro, Laithun
%A Singh, Madan Mohan
%A Goswami, Jituparna
%D 2024
%\ 09/01/2024
%V 12
%N 1
%P 79-89
%! THE UNIT GRAPH OF A COMMUTATIVE SEMIRING
%K Unit graph
%K connectedness
%K diameter
%K girth
%K traversability
%R 10.22044/jas.2022.11957.1612
%X 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.
%U https://jas.shahroodut.ac.ir/article_2836_cf33c9288a9bbc12414f964d9bc4eb79.pdf