Open AccessRoman Domination of Some Chemical Graphs
Author(s) -
Pallavi Sangolli,
Manjula C. Gudgeri,
Varsha Varsha,
Shailaja S. Shirkol
Publication year - 2021
Publication title -
journal of pharmaceutical research international
Language(s) - English
Resource type - Journals
ISSN - 2456-9119
DOI - 10.9734/jpri/2021/v33i47a33045
Subject(s) - vertex (graph theory) , topological index , combinatorics , wiener index , mathematics , quantitative structure–activity relationship , graph , pyrene , function (biology) , connectivity , domination analysis , chemistry , computational chemistry , stereochemistry , organic chemistry , evolutionary biology , biology
The concept of Domination in graphs has application to the study of DNA structures. For investigating the chemical and physical properties, several topological indices used are Wiener index, Randic index, Zagreb index, Kier & Hall index that depends on vertex degree and distance sum, and have been used extensively for QSAR and QSPR studies.
A Roman Dominating Function of G is function f: V→ {0, 1, 2} such that every vertex v for which f (v) = 0 has a neighbor u with f(u) = 2. The weight of a Roman dominating function f is w (f) = . The Roman domination number of a graph G is denoted by (G) and is the minimum weight of all possible Roman dominating functions. In this paper, we find Roman domination number of some chemicals graphs such as saturated hydrocarbons and unsaturated hydrocarbons, hexagonal chain, pyrene, Hexabenzocoronene, H-Phenylenic nanotube and N-Napthelenic nanotube.