Hamiltonian Cycles in Cayley Graphs of Semidirect Products of Finite Groups

G. H J. Lanel, T. M. K. K. Jinasena, B. A. K. Welihinda

Abstract


It has been conjectured that every connected Cayley graph of order greater than 2 has a Hamilton cycle. In this paper, we prove that the Cayley graph of (Zp×Zp)⋊ Zq with respect to a generating set S, Cay((Zp×Zp)⋊ Zq, S), where ={s,t} with |s|=p and |t|=q is Hamiltonian for p,q > 3. Furthermore, the existence of a Hamilton cycle in the Cayley graph of a semidirect product of finite groups is proved by placing restrictions on the generating sets. Consequently, the existence of a Hamilton cycle in the Cayley graphs of several isomorphism types of groups of orders pnq, p2q2 and p2qr, where ≥ 2 is also proved.

Key words: Cayley graph, connected and bridgeless, finite groups, Hamilton cycle, perfect matching, semidirect product, standard generating set.

 


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Copyright (c) 2020 G. H J. Lanel, T. M. K. K. Jinasena, B. A. K. Welihinda

Copyright CC BY © European Modern Studies Journal 2017-2020   ISSN 2522-9400

Лицензия Creative Commons


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