Fractal Graph of Total Regular Fractional Domination Number

Abstract

Determining the new dominance parameter on a fractal graph, called total regular domination, is the main objective of this work. Domination parameters, specifically regular and fractional domination, in fractal network designs are examined in this paper. In order to clarify the properties of a fractal graph, the authors used prior findings to calculate the fractional domination number and related metrics.Finally, mentioned how to apply this new parameter in our real life situation.

Objectives: fractal is an assemblage of precisely defined, asymmetrical, and segmentable structures. There is a relationship between each of these smaller parts.

Methods: Consider a graph G is an undirected graph that is connected. The total regular fractional dominance number of the fractal graph F_G [TRFDN], which is represented as (G), is a new parameter created by this study. to determine the lowest weight when all of the vertices have fractional weights and the dominated vertices are regular.