ABSTRACT: A difference labeling of a graph G is realized by assigning distinct integer values to its vertices and then associating with each edge the absolute difference of those values assigned to its end vertices. A decomposition of labeled graph into parts, each part containing the edge having a commonweight is called a common – weight decomposition. In this paper we investigate the existenc...

Applications of graph and hypergraph decomposition techniques to SAT solving have been studied under various conditions. Theoretical research focused on the direction given by tree decompositions, while practical approaches either integrated tree decomposition guidance into existing SAT solver, or studied splitting techniques using hypergraph cuts. In this article we present a uniform and gener...

We propose a new scalable algorithm that can compute Personalized PageRank (PPR) very quickly. The Power method is a state-of-the-art algorithm for computing exact PPR; however, it requires many iterations. Thus reducing the number of iterations is the main challenge. We achieve this by exploiting graph structures of web graphs and social networks. The convergence of our algorithm is very fast....

We prove that if a graph has a tree-decomposition of width at most w, then it has a tree-decomposition of width at most w with certain desirable properties. We will use this result in a subsequent paper to show that every 2-connected graph of large path-width has a minor isomorphic to either a large tree with a vertex attached to every vertex of the tree or a large outerplanar graph.

In the analysis of organism life cycles in ecology, comparisons of life cycles between species or between different types of life cycles within species are frequently conducted. In matrix population models, partitioning of the elasticity matrix is used to quantify the separate contributions of different life cycles to the population growth rate. Such partition is equivalent to a decomposition o...

In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of th...

Let n ≥ 2 be an integer. The complete graph Kn with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn − F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2, 4 mod 8. We also show that the complete bipartite graph Kn,n has a symmetric Hamilton cycle decomposition if and only if n ...

PHIDAL (Parallel Hierarchical Interface Decomposition ALgorithm) is a parallel incomplete factorization method which exploits a hierarchical interface decomposition of the adjacency graph of the coefficient matrix. The idea of the decomposition is similar to that of the well-known wirebasket techniques used in domain decomposition. However, the method is devised for general, irregularly structu...

In this last of three papers on simplicial tree-decompositions of graphs we investigate the extent to which prime factors in such decompositions are unique, or depend on the decomposition chosen. A simple example shows that a prime decomposition of a graph may have superfluous factors, the omission of which leaves a set of factors that can be rearranged into another decomposition of the same gr...

In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the ...