A graph associated to a commutative semiring

Authors : Shahabaddin Ebrahimi ATANİ, Mehdi KHORAMDEL, Saboura DOLATI PISH HESARI, Mahsa NIKMARD ROSTAM ALIPOUR

Pages : 984-996

Doi:10.31801/cfsuasmas.783398

View : 16 | Download : 7

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :Let R R be a commutative finite semiring with nonzero identity and H H be an arbitrary multiplicatively closed subset R R . The generalized identity-summand graph of R R is the insert ignore into journalissuearticles values(simple); graph G H insert ignore into journalissuearticles values( R ); GHinsert ignore into journalissuearticles values(R); with all elements of R R as the vertices, and two distinct vertices x x and y y are adjacent if and only if x + y ∈ H x+y∈H . In this paper, we study some basic properties of G H insert ignore into journalissuearticles values( R ); GHinsert ignore into journalissuearticles values(R); . Moreover, we characterize the planarity, chromatic number, clique number and independence number of G H insert ignore into journalissuearticles values( R ); GHinsert ignore into journalissuearticles values(R); .
Keywords : I semiring, planar graphs, clique number, chromatic number, independence number