A graph associated to a commutative semiring
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Date
2021
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Ankara Üniversitesi
Abstract
Let R be a commutative finite semiring with nonzero identity and H be an arbitrary multiplicatively closed subset R. The generalized identity-summand graph of R is the (simple) graph GH(R) with all elements of R as the vertices, and two distinct vertices x and y are adjacent if and only if x+y∈H. In this paper, we study some basic properties of GH(R). Moreover, we characterize the planarity, chromatic number, clique number and independence number of GH(R).
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Keywords
I-semiring, planar graphs, clique number, chromatic number, independence number