Laithun Boro - Department of Mathematics, North-Eastern Hill University P.O. Box ۷۹۳۰۲۲, Shillong, India.
Madan Singh - Department of Basic Sciences & Social Sciences, North-Eastern Hill University, P.O. Box ۷۹۳۰۲۲, Shillong, India.
Jituparna Goswami - Department of Mathematics, Gauhati University, P.O. Box ۷۸۱۰۱۴, Guwahati, India.

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.

Unit graph, connectedness, diameter, girth, traversability