Isomorphism of cayley graphs pdf

We study the problem of determining when two cayley graphs on a given abelian group are isomorphic. In this paper, we investigate the isomorphism problems of the generalized cayley graphs, which are generalizations of the traditional cayley graphs. Isomorphisms of generalized cayley graphs yang ars. New york journal of mathematics isomorphisms of cayley graphs. Cayley graphs, their isomorphism problems are well studied in the literature recall that a bicayley graph is a graph which admits a semiregular group of automorphisms with two orbits on the. In 1967, adam 1 conjectured that any two cayley graphs of zn are isomorphic if. We also study the gcigroups among the generalized cayley graphs, and the cayley regressions of some groups. Pdf the cayley isomorphism property for cayley maps. Pdf a combinatorial proof is given for the fact that the cayley graph of the fundamental group. For a positive integer m, the group g is called a connected mdcigroup if for any connected cayley graphs cay g, s and cayg, t of outvalency at most m, s. The isomorphism problem of cayley graphs has been well studied in the literature, such as characterizations of ci dcigraphs and ci dcigroups. Pdf on isomorphisms of connected cayley graphs, iii. Cayley graphs, their isomorphism problems are well studied in the literature recall that a bi cayley graph is a graph which admits a semiregular group of automorphisms with two orbits on the.

Isomorphism and cayley graphs on abelian groups springerlink. Given a finite group g and a symmetric connector set s. We give a sufficient condition to prove that every cayley graph of. We study the problem of determining which cayley graphs and digraphs for a given group are ci graphs. A finite groupgis called aconnected mdcigrouporconnected mcigroup if all connected cayley digraphs or connected cayley graphs. We find that there are two types of natural isomorphisms for the generalized cayley graphs. Pdf isomorphisms of cayley graphs of surface groups.

On isomorphisms of connected cayley graphs, iii article pdf available in bulletin of the australian mathematical society 5801 august 1998 with 47 reads how we measure reads. On isomorphisms of finite cayley graphs a survey core. Isomorphism between z 2 k h and d k k we now prove that every cayley graph on the cyclic group z 2 k is isomorphic to a cayley graph on the dihedral group d k. Request pdf isomorphism between cayley digraphs let. Parsons, isomorphism of circulant graphs, manuscript. Analogously, it is proved that every cayley graph of a cyclic group of order 2k is isomorphic to a cayley graph of the dihedral group dk, and the converse holds if and only if k. Suppose g1 and g2 are torsionfree, nilpotent groups. Isomorphisms of cayley graphs on nilpotent groups dave witte morris, joy morris and gabriel verret abstract.

Cayley graphs of isomorphic groups mathematics stack. Let s be a nite generating set of a torsionfree, nilpotent group g. Which finitely generated abelian groups admit isomorphic cayley. We show that every automorphism of the cayley graph cayg. The isomorphism problem for cayley graphs has been extensively investigated over the past 30 years. The cayley isomorphism property for combinatorial objects was introduced by l.