2021/11/10 by John Baptist Gauci, Gauci, John Baptist, Jean Paul Zerafa +1
Computer Science · Mathematics · #05C60 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2111.05725
openalex publication_date 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2015, Bogdanowicz gave a necessary and sufficient condition for a 4-regular circulant graph to be isomorphic to the Cartesian product of two cycles. Accordion graphs, denoted by A[n,k], are 4-regular graphs on two parameters n and k which were recently introduced by the authors and studied with regards to Hamiltonicity and matchings. These graphs can be obtained by a slight modification in some of the edges of the Cartesian product of two cycles. Motivated by the work of Bogdanowicz, the authors also determined for which values of n and k the accordion graph A[n,k] is circulant. In this work we investigate what parameters a 4-regular circulant graph must have in order to be isomorphic to an accordion graph, thus providing a complete characterisation similar to that given by Bogdanowicz. We also give a necessary and sufficient condition for two accordion graphs with distinct parameters to be isomorphic.