Enhanced Effectiveness in Various Ladder Graphs Based on the F-Centroidal Meanness Criterion

Abstract

Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a richer analysis and interpretation of the graph. Graph labeling in ladder graphs has a wide range of applications in engineering, computer science, physics, biology, and other fields. It can be applied to various problem domains, such as image processing, wireless sensor networks, VLSI design, bioinformatics, social network analysis, transportation networks, and many others. The versatility of ladder graphs and the ability to apply graph labeling to them make them a powerful tool for modeling and analyzing diverse systems. If a function Υ is an injective vertex assignment in {1,2,…q+1} and the inductive edge assignment function Υ* in {1,2,…q} is expressed as a graph with q edges, defined as Υ*(uv)=2[Υ(u)2+Υ(u)Υ(v)+Υ(v)2]3[Υ(u)+Υ(v)], then the function is referred to as F-centroidal mean labeling. This is known as the F-centroidal mean criterion. Here, we have determined the F-centroidal mean criteria of the graph ladder, slanting ladder, triangular ladder, TLn∘Sm, SLn∘Sm for m≤2, double-sided step ladder, Dn*, and diamond ladder.