Let $R$ be a commutative semiring (ring) with identity $1 \neq 0$. A vertex $a$ in a simple graph $G$ is said to be a Smarandache vertex (or S-vertex for short) provided that there exist three distinct vertices $x$, $y$, and $b$ (all different from $a$) in $G$ such that $x$---$a$, $a$---$b$, and $b$---$y$ are edges in $G$, but there is no edge between $x$ and $y$. In this interdisciplinary subject, we investigate the interplay between the algebraic properties of the commutative semirings and their associated zero-divisor graphs, denoted by $\Gamma(R)$, using the notion of the S-vertices in connection with the nonexistence of S-vertices in $\Gamma(R)$. We discuss when $\Gamma(R)$ is a complete bipartite graph together with some of its other graph-theoretic properties and their relation to the nonexistence of S-vertices of $\Gamma(R)$.
Mehdi-Nezhad, E. and Hassan, K. O. E. (2025). Zero-divisor graphs of semirings with no S-vertices. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.29182.1740
MLA
Mehdi-Nezhad, E. , and Hassan, K. O. E. . "Zero-divisor graphs of semirings with no S-vertices", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.29182.1740
HARVARD
Mehdi-Nezhad, E., Hassan, K. O. E. (2025). 'Zero-divisor graphs of semirings with no S-vertices', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.29182.1740
CHICAGO
E. Mehdi-Nezhad and K. O. E. Hassan, "Zero-divisor graphs of semirings with no S-vertices," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.29182.1740
VANCOUVER
Mehdi-Nezhad, E., Hassan, K. O. E. Zero-divisor graphs of semirings with no S-vertices. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.29182.1740
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