THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS

Title & Authors
THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS
Atani, Shahabaddin Ebrahimi; Hesari, Saboura Dolati Pish; Khoramdel, Mehdi;

Abstract
An element r of a commutative semiring R with identity is said to be identity-summand if there exists $\small{1{\neq}a{\in}R}$ such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by $\small{{\Gamma}(R)}$. It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph $\small{{\Gamma}(R)}$ are studied.
Keywords
I-semiring;co-ideal;Q-strong co-ideal;co-semidomain;identity-summand graph;identity-summand element;
Language
English
Cited by
1.
TOTAL GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO IDENTITY-SUMMAND ELEMENTS,;;;

대한수학회지, 2014. vol.51. 3, pp.593-607
2.
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL,;;;

대한수학회지, 2015. vol.52. 1, pp.159-176
1.
TOTAL GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO IDENTITY-SUMMAND ELEMENTS, Journal of the Korean Mathematical Society, 2014, 51, 3, 593
2.
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL, Journal of the Korean Mathematical Society, 2015, 52, 1, 159
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