A stable populations’ network is hard to interrupt without any ecological consequences. A communication blockage between patches may have a negative impact on populations’ stability or it may destabilize the populations in the ecological network. This paper deals with the construction of a safe way passing through the metapopulations habitat such that populations remain stable. To our best know...

altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. we now provide a generalization of the altan concept, applicable to any graph. several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. among these ar...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networ...

In this paper we shall present a simple hybrid model of impact dynamics in heat exchangers. The method, based on graph theory and probability theory, enables us to model the variation in global dynamics as measurable local parameters are changed. We find a sudden jump from no to many repeated impacts, in agreement with numerical and experimental evidence.

The aim of this article is to present a methodological approach for problems encountered in structural analysis of web communities. This approach is based upon the pretopological concepts of pseudoclosure and the searching of equivalent nodes. The advantage of this approach is that it provides a framework needed to pass through the actual limits of graph theory modeling. The problem of modeling...

We derive a simple three parameters conductance formula for wires with monovalent atoms. The functional form of the formula is the most general in the framework of ballistic transport through the chain. The parameters in the formula are related to the nature of the coupling of the wire to the leads and independent of the length of the atomic chain. These parameters can be determined from a firs...

Despite fMRI data being interpreted as time-varying graphs in graph analysis, there has been more emphasis on learning sophisticated node embeddings and complex structures rather than providing a macroscopic description of cortical dynamics. In this paper, I introduce the notion smoothness harmonics to capture slowly varying dynamics graph-based form spatiotemporal patterns. These are rooted ei...

The research that we discuss in this technical report shows that mathematical models of botnet propagation dynamics are a viable means of detecting early stage botnet infections in an enterprise network, and thus an effective tool for containing those botnet infections in a timely fashion. The main idea that underlies this research is to localize weakly connected subgraphs within a graph that m...