Elementary abelian groups of rank 5 are DCI-groups - ScienceDirect Skip to main contentSkip
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In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if $
R $ is a generalised dihedral group and if $ R $ is a CI-group, then for every odd prime $ p …

Let $ m $ be a positive integer. A group $ G $ is said to be an $ m $-BCI-group if $ G $ has
the $ k $-BCI property for all positive integers $ k $ at most $ m $. Let $ G $ be a generalized …

In this paper, we prove several results on the Cayley isomorphism problem concerning
undirected graphs. Let ϕ be Euler's phi function. The main result is the following theorem …

Abstract A Cayley digraph Cay (G, S) of a group G with respect to a subset S of G is called a
CI-digraph if for every Cayley digraph Cay (G, T) isomorphic to Cay (G, S), there exists an …

A group $ G $ is a CI-group with respect to graphs if two Cayley graphs of $ G $ are
isomorphic if and only if they are isomorphic by a group automorphism of $ G $. We show …

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 …

A Cayley digraph Cay (G, S) of a finite group $ G $ with respect to a subset $ S $ of $ G $ is
said to be a CI-digraph if for every Cayley digraph Cay (G, T) isomorphic to Cay (G, S), there …

Let $ m $ be a positive integer. A group $ G $ is said to be an $ m $-DCI-group or an $ m $-
CI-group if $ G $ has the $ k $-DCI property or $ k $-CI property for all positive integers $ k …

A finite group R is a DCI-group if, whenever S and T are subsets of R with the Cayley graphs
Cay (R, S) and Cay (R, T) isomorphic, there exists an automorphism φ of R with S φ= T …