A Hybrid FPT Algorithm Based Domination Topological and Polynomials of a Butterfly Graph

Abstract

In this article, a modified Outer independent Total Roman (OITR) dominating set of the modified simple graph  is a subset of nodes that is both dominant and OITR of the . The novelty consists in calculating the topological dominance indices and their polynomials for different families of Butterfly Graphs (BF) and in graphically representing the different polynomials. In order to improve the domain, the hybrid Fixed-Parameter Tractable (FPT) algorithm with Neuro Fuzzy System controller is proposed. The main purpose of the proposed method is to minimize the dominant ensemble problem and improve performance. FPT with the NFS controller is used to change the OITR settings with the butterfly graph. The advantages of the proposed method are robust performance and maximum reliability and flexibility in solving the problems of the dominant set. Let us examine the independent dominance polynomials of some generalized composite graphs. Then we construct graphs whose roots of the independence domain are real. Also, let's look at some graphs and look at the number of their modified OITR dominant phrases.