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Note on relative Cayley graphs of groups and its complement

Publication Type : Journal Article

Publisher : World Scientific Pub Co Pte Ltd

Source : Discrete Mathematics, Algorithms and Applications

Url : https://doi.org/10.1142/s1793830925500880

Campus : Nagercoil

School : School of Computing

Year : 2025

Abstract : The relative Cayley graph of group [Formula: see text] with respect to its proper subgroup [Formula: see text] is the simple undirected graph with vertex set [Formula: see text] in which two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if [Formula: see text] for some [Formula: see text] where [Formula: see text] is an inversed-closed subset of [Formula: see text]. In this paper, we give a necessary and sufficient condition for [Formula: see text] to be bipartite, complete bipartite, complete, connected, self-centered, star graph, and vertex pancyclic. Also, we give a necessary and sufficient condition for [Formula: see text] to be Eulerian.

Cite this Research Publication : A. Manisekar, S. Anukumar Kathirvel, M. Balamurugan, M. Navaneethakrishnan, Note on relative Cayley graphs of groups and its complement, Discrete Mathematics, Algorithms and Applications, World Scientific Pub Co Pte Ltd, 2025, https://doi.org/10.1142/s1793830925500880

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