Let G be a simple, undirected graph and Gw be the positive weighted graph obtained from G by giving weights to its edges using the positive weight function w. A weighted graph Gw is said to be nonsingular if its adjacency matrix A(Gw) is nonsingular. Let G denote the class of connected, unweighted, bipartite graphs G with a unique perfect matching M such that G/M (the graph obtained by contract...

In this article, only connected bipartite graphs G with a unique perfect matching M are considered. Let Gw denote the weighted graph obtained from G by giving weights to its edges using the positive weight function w : E(G)→ (0,∞) such that w(e) = 1 for each e ∈ M. An unweighted graph G may be viewed as a weighted graph with the weight function w ≡ 1 (all ones vector). A weighted graph Gw is no...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

Weighted graph matching is computationally challenging due to the combinatorial nature of the set of permutations. In this paper, a new relaxation approach to weighted graph matching is proposed, by which a new matching algorithm, named alternate iteration algorithm, is designed. It is proved that the algorithm proposed is locally convergent. Experiments are presented to show the effectiveness ...

Abstract In this chapter, we introduce the mathematical foundations of hypergraph and present notations that are used to facilitate deep understanding analysis structure. A is composed a set vertices hyperedges, it generalization graph, where weighted quantifies relative importance hyperedges or vertices. Hypergraph can also be divided into two main categories, i.e., undirected representation d...

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

In this papel; we present eficient parallel algorithms forjinding a minimum weighted connected dominating set, a minimum weighted Steiner tree for a distance-hereditary graph which take O(1og n) time using O(n+m) processors on a CRCW PRAM, where n and m are the number of vertices and edges of a given graph, respectively. We also find a maximum weighted clique of a distance-hereditary graph in O...