Resumen de Total graph of a commutative semiring with respect to singular ideal

Nabanita Goswami, Helen K. Saikia

• 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(?(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.