Combinatorics and Graph Theory

Study of Roman Domination Number in Deg Centric Graphs

Authors: Kevin Elijah Valentine
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Graph theory plays a vital role in the study of mathematical structures and their applicationsin communication networks, optimization, and computer science. Among the variousdomination parameters, the Double Roman Domination Number has attracted significant attentiondue to its enhanced defensive strategy compared with classical domination concepts.This paper investigates the Double Roman Domination Number of Degree-Centric Graphsobtained from several standard graph families. The degree-centric transformation is firstconstructed for each graph, and the corresponding Double Roman Domination Numbers aredetermined. Based on these results, general observations and formulas are established fordifferent classes of graphs, illustrating the relationship between the degree-centric transformationand the domination parameter. The obtained results extend the study of dominationin transformed graphs and provide a foundation for future research in degree-centric graphtheory.
Category: Combinatorics and Graph Theory