Yuchao Li

Chang'an University · School of Science

A subset F of vertices of a graph G is called a vertex cover P k set if every path of order k in G contains at least one vertex from F. Denote by ψk (G) the minimum cardinality of a vertex cover P k set in G. The vertex cover P k (VCP k ) problem is to find a minimum vertex cover P k set. It is easy to see that the VCP 2 problem corresponds to the...

In graph theory, a (r,s)-fullerene graph is a 3-regular planar graph whose faces are r- or s-gons. Recently, A. Behmaram et al. [MATCH Commun. Math. Comput. Chem. vol. 69, No. 1, 25–32 (2013; Zbl 06274836)] computed the number of paths, matchings and independent sets of low order in (4,6)-fullerene graphs. But, the general form of fullerene graph i...

Given a graph G = (V, E), a matching M of G is a subset of E, such that every vertex of V is incident to at most one edge of M. A k-matching is a matching with k edges. The total number of matchings in G is used in chemoinformatics as a structural descriptor of a molecular graph. Recently, Vesalian and Asgari (MATCH Commun. Math. Comput. Chem. 69 (...

In the connected vertex cover (CVC) problem, we are given a connected graph G and required to find a vertex cover set C with minimum cardinality such that the induced subgraph G[C] is connected. In this paper, we restrict our attention to the CVC problem in 4-regular graphs. We proved that the CVC problem is still NP-hard for 4-regular graphs and g...

Given a connected graph \(G=(V,E)\), the Connected Vertex Cover (CVC) problem is to find a vertex set \(S\subset V\) with minimum cardinality such that every edge is incident to a vertex in S, and moreover, the induced graph G[S] is connected. In this paper, we investigate the CVC problem in k-regular graphs for any fixed k (\(k\ge 4\)). First, we...

The Minimum Weighted Connected Vertex Cover problem (MWCVC) is to find a subset F ⊂ V ( G ) with minimum weight in a node-weighted graph G , such that when removing the set F , the inducing graph of remaining vertices holds no edges, and the graph induced from set F in G is required to be connected. This problem comes from the classi...

This paper introduces a new optimization problem which aims to develop a distribution plan of vaccines which will be supplied over time such that an epidemic can be best suppressed until a complete cure for it is invented. We first exploit the concept of temporal graph to capture the projected images of the evolving social relations over time and f...