On isomorphisms of $m$-Cayley digraphs
Xing Zhang, Yuan-Quan Feng, Fu-Gang Yin, Jin-Xin Zhou

TL;DR
This paper extends the isomorphism problem analysis from Cayley digraphs to $m$-Cayley digraphs, characterizing automorphism groups and classifying certain groups with the CI-property for these generalized structures.
Contribution
It generalizes the normalizer characterization and CI-property concepts from Cayley digraphs to $m$-Cayley digraphs, providing classifications of $m$DCI- and $m$PDCI-groups.
Findings
Characterized the normalizer of $G$ in automorphism groups of $m$-Cayley digraphs
Generalized CI-property concepts to $m$-Cayley digraphs
Classified finite $m$DCI- and $m$PDCI-groups for specific $m$ values
Abstract
The isomorphism problem for digraphs is a fundamental problem in graph theory. This problem for Cayley digraphs has been extensively investigated over the last half a century. In this paper, we consider this problem for -Cayley digraphs which are generalization of Cayley digraphs. Let be a positive integer. A digraph admitting a group of automorphisms acting semiregularly on the vertices with exactly orbits is called an -Cayley digraph of . In particular, -Cayley digraph is just the Cayley digraph. We first characterize the normalizer of in the full automorphism group of an -Cayley digraph of a finite group . This generalizes a similar result for Cayley digraph achieved by Godsil in 1981. Then we use this to study the isomorphisms of -Cayley digraphs. The CI-property of a Cayley digraph (CI stands for `Cayley isomorphism') and the DCI-groups (whose…
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Graph theory and applications
