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
Notes on the connectivity of Cayley coset digraphs
Hamidoune's connectivity results for hierarchical Cayley digraphs are
extended to Cayley coset digraphs and thus to arbitrary vertex transitive
digraphs. It is shown that if a Cayley coset digraph can be hierarchically
decomposed in a certain way, then it is optimally vertex connected. The results
are obtained by extending the methods used by Hamidoune. They are used to show
that cycle-prefix graphs are optimally vertex connected. This implies that
cycle-prefix graphs have good fault tolerance properties.Comment: 15 page
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