On computing a conditional edge-connectivity of a graph
Information Processing Letters
Sufficient conditions for graphs to be λ′-optimal and super-λ′
Networks - Dedicated to Leonhard Euler (1707–1783)
Diameter-sufficient conditions for a graph to be super-restricted connected
Discrete Applied Mathematics
On the 3-restricted edge connectivity of permutation graphs
Discrete Applied Mathematics
Super restricted edge connected Cartesian product graphs
Information Processing Letters
Topological Structure and Analysis of Interconnection Networks
Topological Structure and Analysis of Interconnection Networks
The k-Restricted Edge Connectivity of Balanced Bipartite Graphs
Graphs and Combinatorics
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For a connected graph G, an edge-cut S is called a restricted edge-cut if G-S contains no isolated vertices. And G is said to be super restricted edge-connected, for short super-@l^', if each minimum restricted edge-cut of G isolates an edge. Let V"@d denote the set of the minimum degree vertices of G. In this paper, for a super-@l^' graph G with diameter D=2 and minimum degree @d=4, we show that the induced subgraph G[V"@d] contains no complete graph K"@d"-"1. Applying this property we characterize the super restricted edge connected graphs with diameter 2 which satisfy a type of neighborhood condition. This result improves the previous related one which was given by Wang et al. [S. Wang, J. Li, L. Wu, S. Lin, Neighborhood conditions for graphs to be super restricted edge connected, Networks 56 (2010) 11-19].