Some new approaches to neighborhoods via graphs

Abstract

This paper aims to increase the accuracy measure of the subgraph of a graph and generate new nano topologies on the power set of vertices and edges of a graph. Firstly we introduce E<inf>j</inf>-neighborhoods and C<inf>j</inf>-neighborhoods which depend on vertices and edges of a simple directed graph by using j-neighborhoods for j∈ { out in ∩ ∪ }. Then we apply these neighborhoods to present the concepts of E<inf>j</inf>-approximations and C<inf>j</inf>-approximations. We investigate their main properties and relationships among them. Besides we define the accuracy measures of a subgraph with the help of these approximations and show that C<inf>j</inf>-accuracy measures are the highest when we compare these accuracy measures with the previous one. Furthermore we generate new nano topologies via obtained approximations and illustrate that these topologies may not be comparable. Finally we give an application in physics to elucidate the current approximations are more general. Throughout the paper we summarize all comparisons with tables and give counterexamples to support the study. © 2023 Elsevier B.V. All rights reserved.