436 research outputs found
Large butterfly Cayley graphs and digraphs
We present families of large undirected and directed Cayley graphs whose
construction is related to butterfly networks. One approach yields, for every
large and for values of taken from a large interval, the largest known
Cayley graphs and digraphs of diameter and degree . Another method
yields, for sufficiently large and infinitely many values of , Cayley
graphs and digraphs of diameter and degree whose order is exponentially
larger in than any previously constructed. In the directed case, these are
within a linear factor in of the Moore bound.Comment: 7 page
A family of mixed graphs with large order and diameter 2
A mixed regular graph is a connected simple graph in which each vertex has both a fixed outdegree (the same indegree) and a fixed undirected degree. A mixed regular graphs is said to be optimal if there is not a mixed regular graph with the same parameters and bigger order.
We present a construction that provides mixed graphs of undirected degree qq, directed degree View the MathML sourceq-12 and order 2q22q2, for qq being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to View the MathML source9q2-4q+34 the defect of these mixed graphs is View the MathML source(q-22)2-14.
In particular we obtain a known mixed Moore graph of order 1818, undirected degree 33 and directed degree 11 called Bosák’s graph and a new mixed graph of order 5050, undirected degree 55 and directed degree 22, which is proved to be optimal.Peer ReviewedPostprint (author's final draft
Edge modification criteria for enhancing the communicability of digraphs
We introduce new broadcast and receive communicability indices that can be
used as global measures of how effectively information is spread in a directed
network. Furthermore, we describe fast and effective criteria for the selection
of edges to be added to (or deleted from) a given directed network so as to
enhance these network communicability measures. Numerical experiments
illustrate the effectiveness of the proposed techniques.Comment: 26 pages, 11 figures, 4 table
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