Computational
Method based on NonNodal Graph Expansion for Directed Percolation
Model
Faqir M Bhatti
fmbhatti@lums.edu.pk
Mathematics
Lahore University of Management Sciences
Pakistan
Abstract
A simple two rooted acyclic directed graph in which each element
(vertex or site) is assigned one of the states ?pen?or ?losed?with
probability p or (1p) respectively independently of all other elements
is called a Directed Percolation Model. The uv backbone in any
configuration is the subgraphs consisting of all elements which
belong to at least one open path from a root u to a root v in the
directed graph. The properties of this backbone in the case that
G is a directed graph representing a lattice are important in understanding
various properties of directed percolation model. The purpose of
this article is to present a computational method which is based
on two rooted acyclic nonnodal directed graphs expansion (graph
without articulation point) which involves Moboius function. We
present various properties of the percolation model including flicker
noise by analyzing the series with Mathematica software.
