Perfect matching and distance spectral radius in graphs and bipartite graphs

Spectral radius of bipartite graphs

On the distance spectral radius of bipartite graphs

Article history: Received 11 June 2011 Accepted 29 July 2011 Available online 27 August 2011 Submitted by R.A. Brualdi AMS classification: 05C50 15A18

The labeled perfect matching in bipartite graphs

In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V,E) with |V | = 2n vertices such that E contains a perfect matching (of size n), together with a color (or label) function L : E → {c1, . . . , cq}, the labeled perfect matching problem consists in finding a perfect matching on G that us...

On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

Bipartite Graphs and Perfect Matchings

When we think about markets creating opportunities for interaction between buyers and sellers, there is an implicit network encoding the access between buyers and sellers. In fact, there are several ways to use networks to model buyer-seller interaction, and here we discuss some of them. First, consider the case in which not all buyers have access to all sellers. There could be several reasons ...