What question did this study set out to answer?

The research aims to establish conditions that determine when generalized Cayley graphs of finite groups are bipartite and connected.

May 27, 2026Open Access

On structural properties of generalized Cayley graphs

Key Points

The research aims to establish conditions that determine when generalized Cayley graphs of finite groups are bipartite and connected.
Analyzed structural properties of generalized Cayley graphs of finite abelian groups.
Formulated necessary and sufficient conditions for bipartiteness and connectivity.
Identified groups with connected and integral cubic generalized Cayley graphs.
Provided explicit conditions for bipartite generalized Cayley graphs of finite abelian groups.
Derived multiple conditions for determining the connectedness of generalized Cayley graphs.
Identified specific groups where all cubic generalized Cayley graphs are both connected and integral.

Abstract

In this paper, firstly, we provide some necessary and sufficient conditions for generalized Cayley graphs of finite abelian groups to be bipartite. Secondly, we deduce several necessary and sufficient conditions for generalized Cayley graphs of finite groups to be connected. At last, as a by-product, we determine the groups whose all cubic generalized Cayley graphs are connected and integral.

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