80 research outputs found
On finite groups all of whose cubic Cayley graphs are integral
For any positive integer , let denote the set of finite
groups such that all Cayley graphs are integral whenever
. Estlyi and Kovcs \cite{EK14}
classified for each . In this paper, we characterize
the finite groups each of whose cubic Cayley graphs is integral. Moreover, the
class is characterized. As an application, the classification
of is obtained again, where .Comment: 11 pages, accepted by Journal of Algebra and its Applications on June
201
Finite groups whose commuting graph is split
As a contribution to the study of graphs defined on groups, we show that for a finite group G the following statements are equivalent: the commuting graph of G is a split graph; the commuting graph of G is a threshold graph; either G is abelian, or G is a generalized dihedral group D(A)=β¨A,t:(βaβA)(at)2=1β© where A is an abelian group of odd order.Peer reviewe
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