9,703 research outputs found
Large Networks of Diameter Two Based on Cayley Graphs
In this contribution we present a construction of large networks of diameter
two and of order for every degree , based on Cayley
graphs with surprisingly simple underlying groups. For several small degrees we
construct Cayley graphs of diameter two and of order greater than of
Moore bound and we show that Cayley graphs of degrees
constructed in this paper are the largest
currently known vertex-transitive graphs of diameter two.Comment: 9 pages, Published in Cybernetics and Mathematics Applications in
Intelligent System
Fractional revival on semi-Cayley graphs over abelian groups
In this paper, we investigate the existence of fractional revival on
semi-Cayley graphs over finite abelian groups. We give some necessary and
sufficient conditions for semi-Cayley graphs over finite abelian groups
admitting fractional revival. We also show that integrality is necessary for
some semi-Cayley graphs admitting fractional revival. Moreover, we characterize
the minimum time when semi-Cayley graphs admit fractional revival. As
applications, we give examples of certain Cayley graphs over the generalized
dihedral groups and generalized dicyclic groups admitting fractional revival
Cayley Graphs of Groups and Their Applications
Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the change ringing of bells)
Integral Cayley graphs over a group of order
In this paper, we study the integral Cayley graphs over a non-abelian group
of order . We
give a necessary and sufficient condition for the integrality of Cayley graphs
over . We also study relationships between the integrality of Cayley
graphs over and the Boolean algebra of cyclic groups. As applications,
we construct some infinite families of connected integral Cayley graphs over
Fractional revival on Cayley graphs over abelian groups
In this paper, we investigate the existence of fractional revival on Cayley
graphs over finite abelian groups. We give a necessary and sufficient condition
for Cayley graphs over finite abelian groups to have fractional revival. As
applications, the existence of fractional revival on circulant graphs and
cubelike graphs are characterized
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
Coupling and Bernoullicity in random-cluster and Potts models
An explicit coupling construction of random-cluster measures is presented. As
one of the applications of the construction, the Potts model on amenable Cayley
graphs is shown to exhibit at every temperature the mixing property known as
Bernoullicity
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