We prove comparison results for the Swendsen-Wang (SW) dynamics, the heat-bath (HB) dynamics for the Potts model and the single-bond (SB) dynamics for the randomcluster model on arbitrary graphs. In particular, we prove that rapid (i.e. polynomial) mixing of HB implies rapid mixing of SW on graphs with bounded maximum degree and that rapid mixing of SW and rapid mixing of SB are equivalent. Add...

In dynamic force spectroscopy, a (bio-)molecular complex is subjected to a steadily increasing force until the chemical bond breaks. Repeating the same experiment many times results in a broad distribution of rupture forces, whose quantitative interpretation represents a formidable theoretical challenge. In this study we address the situation that more than a single molecular bond is involved i...

Abstract In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models random graphs when considered at criticality. Specifically, apply our method model intersection graph, graph obtained through p -bond percolation on general d -regular and an inhomogeneous graph.

A computer code based on the Givens-Householder matrix diagonalization method is used to calculate the spectra of graphs containing a large number of vertices. The code is most general in that it can handle graphs containing 200 or more vertices. Further, the code can be used to generate the spectra of weighted graphs. The program requires as input only the neighborhood table of the graph. The ...

The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations have been carried out in the past several years. In this note we first consider graphs with given edge-connectivity that attain the maximum ABC index. In pa...

Inspired by empirical studies researchers have tried to model various systems like human populations, the World Wide Web or electric power grids by random graphs. Here we first examine different properties of random graphs(both undirected and directed) having arbitrary degree distributions using the generating functon formalism. We present some empirical data about the structure of random graph...

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...