On computing a conditional edge-connectivity of a graph
Information Processing Letters
Extraconnectivity of graphs with large girth
Discrete Mathematics - Special issue on graph theory and applications
Edge-cuts leaving components of order at least three
Discrete Mathematics
Sufficient conditions for λ′-optimality in graphs with girth g
Journal of Graph Theory
Graph Theory
On the 3-restricted edge connectivity of permutation graphs
Discrete Applied Mathematics
A neighborhood condition for graphs to be maximally k-restricted edge connected
Information Processing Letters
| Hi-index | 0.04 |
For a connected graph G=(V,E), an edge set S@?E is a k-restricted edge cut if G-S is disconnected and every component of G-S has at least k vertices. The k-restricted edge connectivity of G, denoted by @l"k(G), is defined as the cardinality of a minimum k-restricted edge cut. Let @x"k(G)=min{|[X,X@?]|:|X|=k,G[X] is connected}. G is @l"k-optimal if @l"k(G)=@x"k(G). In 2004, Hellwig and Volkmann gave a sufficient condition for @l"2-optimality in graphs of diameter 2. In this paper, we extend the result and give a similar sufficient condition for @l"k-optimality in graphs of diameter 2 with k=3.