Total graph of a commutative semiring with respect to singular ideal
Abstract: Let S be a commutative semiring with unity. The singular ideal Z(S) of S is defined as Z(S) = {s ∈ S | sK = 0 for some essential ideal K of S}. In this paper, we introduce the notion of total graph of a commutative semiring with respect to the singular ideal. We define this graph...
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| Autores principales: | , |
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000300517 |
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| Sumario: | Abstract: Let S be a commutative semiring with unity. The singular ideal Z(S) of S is defined as Z(S) = {s ∈ S | sK = 0 for some essential ideal K of S}. In this paper, we introduce the notion of total graph of a commutative semiring with respect to the singular ideal. We define this graph as the undirected graph T(Γ(S)) with all elements of S as vertices and any two distinct vertices x and y are adjacent if and only if x+y ∈ Z(S). We discuss various characteristics of this total graph and also characterize some important properties of certain induced subgraphs of this total graph. |
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