The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph, which is proposed first by Gutman and Wagner [The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177–2187]. And they gave some properties and asymptotic results of the matching energy. In this paper, we characterize the trees with n vertices whose complements have t...

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...

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph G = (A ∪ P,E) such that A denotes a set of applicants and P a set of posts. Each applicant a ∈ A has a preference list over the set of his neighbors in G, possibly involving ties. Preference lists are represented by ranks on the edges an edge (a, p) has ...

An induced matching M of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M . The MINIMUM MAXIMAL INDUCED MATCHING problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complete. Here we show that, if P 6= NP, for any ε >...

A matching M of a graph G is maximal if it not proper subset any other in G. Maximal matchings are much less known and researched than their maximum perfect counterparts. In this paper we present the recurrences generating functions for sequences enumerating two classes chemically interesting linear polymers: polyspiro chains benzenoid chains. We also analyze asymptotic behavior those determine...

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributedmemory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal match...

Given two graphs, a fundamental task faced by matching algorithms consists of computing either the (Connected) Maximal Common Induced Subgraphs ((C)MCIS) or the (Connected) Maximal Common Edge Subgraphs ((C)MCES). In particular, computing the CMCIS or CMCES reduces to reporting so-called connected cliques in product graphs, a problem for which an algorithm has been presented in a recent paper I...