The depletion of natural resources in the last century now threatens our planet and the life of future generations. For the sake of sustainable development, this paper pioneers an interesting and practical problem of dense substructure (i.e., maximal cliques) mining in a fuzzy graph where the edges are weighted by the degree of membership. For parameter 0 ≤ λ ≤ 1 (also called fuzzy cut in fuzzy...

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input graph G without cycles of length 4, 5, and 6, we cha...

Let P be a graph property which is preserved by removal of edges. A random maximal P-graph is obtained from n independent vertices by randomly adding edges, at each stage choosing uniformly among edges whose inclusion would not destroy property P, until no further edges can be added. We address the question of the number of edges of a random maximal P-graph for several properties P, in particul...

Let G be a simple connected graph on n vertices and λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G. The Estrada index of G is defined as EE(G) = Σ i=1 ei . A cactus is a connected graph in which any two cycles have at most one common vertex. In this work, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cycles was determined. Also, ...

It is well known that the problem of matching two relational structures can be posed as an equivalent problem of nding a maximal clique in a (derived) \association graph." However, it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized, i.e. are trees, since maximal cliques are not constrained to preserve the partial order. Here we p...

For guaranteeing all multicast destination nodes receiving the source information with their maximal flow respectively and obtaining the network maximal throughput, a heuristic algorithm based on network coding, Maximal Flow for Single-source Two-destinations Multicast (MFSTM) is proposed to maximize the network throughput. By calculating the each destination’s maximal flow, the number of linkd...

Recent advances in computer vision, information retrieval, and molecular biology amply demonstrate the value and importance of graph matching. However, graph matching algorithms developed to date are either application domainspecific or severely limited by the problem size. This paper presents a unified solution for the broad range of major graph matching problems. Particularly, the new algorit...

Albertson [3] has defined the irregularity of a simple undirected graph G = (V,E) as irr(G) = ∑ uv∈E |dG(u)− dG(v)| , where dG(u) denotes the degree of a vertex u ∈ V . Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [13]. For general graphs with n vertices...

A perfect transversal of a graph is a set of vertices that meets any maximal clique, or any maximal stable set of the graph in exactly one vertex. In this paper we give some properties of perfect transversals in graph products. One of these properties is the characterization of the existence of perfect transversals in some graph products via perfect transversals of the factors. As an applicatio...

We study some counting and enumeration problems for chordal graphs, especially concerning independent sets. We first provide the following efficient algorithms for a chordal graph: (1) a linear-time algorithm for counting the number of independent sets; (2) a linear-time algorithm for counting the number of maximum independent sets; (3) a polynomial-time algorithm for counting the number of ind...