A Family of Tetravalent Half-transitive Graphs

TL;DR

This paper introduces an infinite family of tetravalent half-transitive Cayley graphs, expanding understanding of their structural properties and classifications.

Contribution

It presents a new family of graphs, $ ext{Gamma}(n,a)$, demonstrating their half-transitive Cayley graph structure and analyzing their properties.

Findings

$ ext{Gamma}(n,a)$ is an infinite family of tetravalent half-transitive Cayley graphs.

Structural properties of $ ext{Gamma}(n,a)$ are characterized.

The family broadens the classification of half-transitive graphs.

Abstract

In this paper, we introduce a new family of graphs, $\Gamma(n,a)$. We show that it is an infinite family of tetravalent half-transitive Cayley graphs. Apart from that, we determine some structural properties of $\Gamma(n,a)$.