THE UNIT GRAPH OF A COMMUTATIVE SEMIRING | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 79-89 اصل مقاله (144.08 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11957.1612 | ||
| نویسندگان | ||
| Laithun Boro* 1؛ Madan Mohan Singh2؛ Jituparna Goswami3 | ||
| 1Department of Mathematics, North-Eastern Hill University P.O. Box 793022, Shillong, India. | ||
| 2Department of Basic Sciences & Social Sciences, North-Eastern Hill University, P.O. Box 793022, Shillong, India. | ||
| 3Department of Mathematics, Gauhati University, P.O. Box 781014, Guwahati, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Unit graph؛ connectedness؛ diameter؛ girth؛ traversability | ||
| مراجع | ||
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