Roughness in Cayley Graphs

TL;DR

This paper introduces rough and pseudo-Cayley graphs, expanding algebraic graph theory with rough approximation concepts, and explores properties like connectivity, opening new research avenues in data networks.

Contribution

It proposes new algebraic structures called pseudo-Cayley graphs and extends rough approximation methods to these graphs, providing foundational theorems and properties.

Findings

Defined rough edge Cayley graphs and pseudo-Cayley graphs.

Derived properties like connectivity and optimal connectivity.

Established theorems expanding algebraic graph theory.

Abstract

In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is expanded to pseudo-Cayley graphs. Also, rough vertex pseudo-Cayley graphs and rough pseudo-Cayley graphs are introduced. Some theorems are provided, form which some properties such as connectivity and optimal connectivity are derived. This approach opens a new research field in sciences such as data networks.