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<p>We investigate Cayley graphs of graph products of groups. We prove that if the vertex groups admit isomorphic Cayley graphs with respect to chosen symmetric generating sets, then the associated graph products have isomorphic Cayley graphs with respect to induced generating sets. Then we provide examples of non-isomorphic graph products of finite groups whose Cayley graphs are nevertheless isomorphic.</p>

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Some groups with Isomorphic Cayley Graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月15日

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  • Marjory Mwanza

摘要

We investigate Cayley graphs of graph products of groups. We prove that if the vertex groups admit isomorphic Cayley graphs with respect to chosen symmetric generating sets, then the associated graph products have isomorphic Cayley graphs with respect to induced generating sets. Then we provide examples of non-isomorphic graph products of finite groups whose Cayley graphs are nevertheless isomorphic.