20,706 research outputs found
On the super connectivity of Kronecker products of graphs
In this paper we present the super connectivity of Kronecker product of a
general graph and a complete graph.Comment: 8 page
Connectivity of Direct Products of Graphs
Let be the connectivity of and the direct product
of and . We prove that for any graphs and with ,
, which was conjectured
by Guji and Vumar.Comment: 5 pages, accepted by Ars Com
On the diameter of the Kronecker product graph
Let and be two undirected nontrivial graphs. The Kronecker
product of and denoted by with vertex set
, two vertices and are adjacent if and
only if and . This paper presents a
formula for computing the diameter of by means of the
diameters and primitive exponents of factor graphs.Comment: 9 pages, 18 reference
Information Super-Diffusion on Structured Networks
We study diffusion of information packets on several classes of structured
networks. Packets diffuse from a randomly chosen node to a specified
destination in the network. As local transport rules we consider random
diffusion and an improved local search method. Numerical simulations are
performed in the regime of stationary workloads away from the jamming
transition. We find that graph topology determines the properties of diffusion
in a universal way, which is reflected by power-laws in the transit-time and
velocity distributions of packets. With the use of multifractal scaling
analysis and arguments of non-extensive statistics we find that these
power-laws are compatible with super-diffusive traffic for random diffusion and
for improved local search. We are able to quantify the role of network topology
on overall transport efficiency. Further, we demonstrate the implications of
improved transport rules and discuss the importance of matching (global)
topology with (local) transport rules for the optimal function of networks. The
presented model should be applicable to a wide range of phenomena ranging from
Internet traffic to protein transport along the cytoskeleton in biological
cells.Comment: 27 pages 7 figure
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