Provides conditions for bipartiteness and connectivity in finite group Cayley graphs, highlighting significance.
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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Liao et al. (2025) studied this question.
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