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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Universidad Católica del Norte, Departamento de Matemáticas
2020
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oai:scielo:S0716-091720200003005172020-06-17Total graph of a commutative semiring with respect to singular idealGoswami,NabanitaSaikia,Helen K. Semiring Total graph Singular ideal Induced Subgraphs 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.3 20202020-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000300517en10.22199/issn.0717-6279-2020-03-0032 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Semiring Total graph Singular ideal Induced Subgraphs |
| spellingShingle |
Semiring Total graph Singular ideal Induced Subgraphs Goswami,Nabanita Saikia,Helen K. Total graph of a commutative semiring with respect to singular ideal |
| description |
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. |
| author |
Goswami,Nabanita Saikia,Helen K. |
| author_facet |
Goswami,Nabanita Saikia,Helen K. |
| author_sort |
Goswami,Nabanita |
| title |
Total graph of a commutative semiring with respect to singular ideal |
| title_short |
Total graph of a commutative semiring with respect to singular ideal |
| title_full |
Total graph of a commutative semiring with respect to singular ideal |
| title_fullStr |
Total graph of a commutative semiring with respect to singular ideal |
| title_full_unstemmed |
Total graph of a commutative semiring with respect to singular ideal |
| title_sort |
total graph of a commutative semiring with respect to singular ideal |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2020 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000300517 |
| work_keys_str_mv |
AT goswaminabanita totalgraphofacommutativesemiringwithrespecttosingularideal AT saikiahelenk totalgraphofacommutativesemiringwithrespecttosingularideal |
| _version_ |
1718439871468535808 |