TY - JOUR
ID - 2836
TI - THE UNIT GRAPH OF A COMMUTATIVE SEMIRING
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Boro, Laithun
AU - Singh, Madan Mohan
AU - Goswami, Jituparna
AD - Department of Mathematics, North-Eastern Hill University P.O. Box 793022,
Shillong, India.
AD - Department of Basic Sciences & Social Sciences, North-Eastern Hill University,
P.O. Box 793022, Shillong, India.
AD - Department of Mathematics, Gauhati University, P.O. Box 781014, Guwahati,
India.
Y1 - 2024
PY - 2024
VL - 12
IS - 1
SP - 79
EP - 89
KW - Unit graph
KW - connectedness
KW - diameter
KW - girth
KW - traversability
DO - 10.22044/jas.2022.11957.1612
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_2836.html
L1 - https://jas.shahroodut.ac.ir/article_2836_cf33c9288a9bbc12414f964d9bc4eb79.pdf
ER -