TY - JOUR AU - Goswami, Nabanita AU - Saikia, Helen K. PY - 2020/06/03 Y2 - 2024/03/28 TI - Total graph of a commutative semiring with respect to singular ideal JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 39 IS - 3 SE - DO - 10.22199/issn.0717-6279-2020-03-0032 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3717 SP - 517-527 AB - <p><em>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.</em></p> ER -