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

Authors:
Weihua Yang;Yingzhi Tian;Hengzhe Li;Hao Li;Xiaofeng Guo
Affiliations:
-;-;-;-;-
Venue:
Discrete Applied Mathematics
Year:
2014

Citing 4
Cited 0

On computing a conditional edge-connectivity of a graph

Information Processing Letters
On minimum critically n-edge-connected graphs

SIAM Journal on Algebraic and Discrete Methods
On restricted edge-connectivity of graphs

Discrete Mathematics
Graph Theory With Applications

Graph Theory With Applications

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Abstract

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=uv@?E(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 @d and a given minimum edge-degree 2@d+k-2. Moreover, we characterize the extremal graphs for k=0,1,2. As an application, we characterize some kinds of minimum restricted edge connected graphs.