Eman Rawshdeh, Heba Adel Abdelkarim, Edris Rawashdeh, "Some Properties of Unit Graphs of Rings," WSEAS Transactions on Mathematics, vol. 25, pp. 78-85, 2026, DOI:10.37394/23206.2026.25.9
Eman Rawshdeh, Heba Adel Abdelkarim, Edris Rawashdeh. Some Properties of Unit Graphs of Rings.
WSEAS Transactions on Mathematics. 2026;25:78-85. 10.37394/23206.2026.25.9
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Some Properties of Unit Graphs of Rings
Authors: , ,
Abstract: Let $$ R $$ be a ring with a nonzero identity. The unit graph $$ G(R) $$ is defined in such a way that $$ R $$ is the vertex set of $$ G(R), $$ where the adjacency of two different vertices depends on their sum being a unit in $$ R. $$ In this paper, the spectrum of $$ G(R_1) $$ and $$ G(R_2) $$ where $$ R_1 =Z_p(+) Z_p $$ and $$ R_2 = Z_{p^2}(+)Z_{p^2} $$ has been determined. In addition, the eigenvalue property of $$ G(R_2) $$ has been studied. Finally, the Wiener index $$ W(G) $$ of unit graphs $$ G(R_1) $$ and $$ G(R_2) $$ has been evaluated.
Keywords:
Commutative Ring, Unit Graph, Wiener index of a graph, Biclique decomposition number, Eigensharp graph
Pages: 78-85 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 25, 2026, Art. #9 DOI: 10.37394/23206.2026.25.9
×
Citation Tools