Open AccessDegree coprime domination and degree non-coprime domination in graphs
Author(s) -
B Guruprakasam,
M Anitha,
S. Balamurugan
Publication year - 2022
Publication title -
international journal of health sciences (ijhs) (en línea)
Language(s) - English
Resource type - Journals
eISSN - 2550-6978
pISSN - 2550-696X
DOI - 10.53730/ijhs.v6ns2.6270
Subject(s) - coprime integers , degree (music) , combinatorics , vertex (graph theory) , mathematics , domination analysis , dominating set , graph , simple graph , undirected graph , discrete mathematics , physics , acoustics
Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(G) is called a degree coprime dominating set of G if for every v∈V-D, there exist a vertex u∈D such that uv∈E(G) and (deg u,deg v)=1. The minimum cardinality of a degree coprime dominating set is called the degree coprime domination number of G and is denoted by γ_cp (G). A dominating set D of V(G) is called a degree non-coprime dominating set of G if for every v∈V-D, there exist a vertex u∈D such that uv∈E(G) and (deg u,deg v)≠1. The minimum cardinality of a degree non-coprime dominating set is called the degree non-coprime domination number and is denoted by γ_ncp (G). We obtain the degree coprime domination number for some graphs.