Article Dans Une Revue Discrete Applied Mathematics Année : 2014

The minimum restricted edge-connected graph and the minimum size of graphs with a given edge–degree

Résumé

Let G=(V(G),E(G)) be a graph. Determining the minimum and/or maximum size (|E(G)|) of graphs with some given parameters is a classic extremal problem in graph theory. For a graph G and e=uvE(G), we denote d(e)=d(u)+d(v)2 the edge–degree of e. In this paper, we obtain a lower bound for the minimum size of graphs with a given order n, a given minimum degree δ and a given minimum edge–degree 2δ+k2. Moreover, we characterize the extremal graphs for k=0,1,2. As an application, we characterize some kinds of minimum restricted edge connected graphs.

Dates et versions

hal-01132310 , version 1 (17-03-2015)

Identifiants

Citer

Weihua Yang, Yingzhi Tian, Hengzhe Li, Hao Li, Xiaofeng Guo. The minimum restricted edge-connected graph and the minimum size of graphs with a given edge–degree. Discrete Applied Mathematics, 2014, 167, pp.304-309. ⟨10.1016/j.dam.2013.10.028⟩. ⟨hal-01132310⟩
67 Consultations
0 Téléchargements

Altmetric

Partager

More