In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable stat...

In this paper, we propose an image segmentation method based on morphological decomposition and graph-based region merging using contour dynamics. The input image is initially decomposed into a set of primitive homogeneous regions through the morphological watershed transform applied to the image intensity gradient magnitude. This decomposition is represented by a Region Adjacency Graph (RAG) t...

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of visibility graph motifs, smaller substructures that appear with characteristic frequencies. We develop ...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

Human big conductance Caand voltage-gated K channels (hBK) are putative drug targets for cardiovascular, respiratory and urological diseases. Here we have used molecular simulation and bioinformatics approaches to construct models of two domains important for Ca binding and channel gating, namely the regulator of conductance for K (RCK1) domain and the so-called calcium bowl (CB). As templates ...

Bond graphs have established themselves as a reliable tool for modeling physical systems. Multi-bonds are a bondgraphic extension that provides a general approach to modeling all kinds of multi-dimensional processes in continuous physical systems. This paper presents a Modelica library for modeling multi-bond graphs and their application to three-dimensional mechanical systems. A set of bondgra...

Understanding and controlling spreading dynamics in networks presupposes the identification of those influential nodes that will trigger an efficient information diffusion. It has been shown that the best spreaders are the ones located in the core of the network – as produced by the k-core decomposition. In this paper we further refine the set of the most influential nodes, showing that the nod...

We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the system can be completely solved, due to the asymptotic absence of loops. For arbitrary graph symmetry, we solve the dynamics exactly for the first few time s...