Dominator semi strong color partition in graphs

Authors : Praba VENKATRENGAN, Swaminathan VENKATASUBRAMANIAN, Raman SUNDARESWARAN

Pages : 930-943

Doi:10.31801/cfsuasmas.1014919

View : 19 | Download : 6

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :Let G G = insert ignore into journalissuearticles values( V , E ); insert ignore into journalissuearticles values(V,E); be a simple graph. A subset S S is said to be Semi-Strong if for every vertex v v in V V , | N insert ignore into journalissuearticles values( v ); ∩ S | ≤ 1 |Ninsert ignore into journalissuearticles values(v);∩S|≤1 , or no two vertices of S S have the same neighbour in V V , that is, no two vertices of S S are joined by a path of length two in V V . The minimum cardinality of a semi-strong partition of G G is called the semi-strong chromatic number of G G and is denoted by χ s G χsG . A proper colour partition is called a dominator colour partition if every vertex dominates some colour class, that is , every vertex is adjacent with every element of some colour class. In this paper, instead of proper colour partition, semi-strong colour partition is considered and every vertex is adjacent to some class of the semi-strong colour partition.Several interesting results are obtained.
Keywords : Dominator coloring, semi strong color partition, semi strong coloring