On computing a conditional edge-connectivity of a graph
Information Processing Letters
Connectivity of generalized prisms over G
ARIDAM III Selected papers on Third advanced research institute of discrete applied mathematics
Extraconnectivity of graphs with large girth
Discrete Mathematics - Special issue on graph theory and applications
Large survivable nets and the generalized prisms
Discrete Applied Mathematics
On the extraconnectivity of graphs
Discrete Mathematics - Special issue on combinatorics
On connectivity of the Cartesian product of two graphs
Applied Mathematics and Computation
Edge-cuts leaving components of order at least three
Discrete Mathematics
On the edge-connectivity and restricted edge-connectivity of a product of graphs
Discrete Applied Mathematics
Sufficient conditions for λ′-optimality in graphs with girth g
Journal of Graph Theory
On the 3-restricted edge connectivity of permutation graphs
Discrete Applied Mathematics
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This work deals with a generalization of the Cartesian product of graphs, the product graph G"m*G"p introduced by Bermond et al. [J.C. Bermond, C. Delorme, G. Farhi, Large graphs with given degree and diameter II, J. Combin. Theory, Series B 36 (1984), 32-48]. The connectivity of these product graphs is approached by studying the k-restricted edge-connectivity, which is defined as the minimum number of edges of a graph whose deletion yields a disconnected graph with all its components having at least k vertices. To be more precise, we present lower and upper bounds for the k-restricted edge-connectivity of G"m*G"p, and provide sufficient conditions that ensure an optimal value for this parameter. When both G"m and G"p are regular graphs, conditions for guaranteeing that G"m*G"p is super-@l"("k") are also presented, and the particular case where both G"m and G"p are complete graphs is considered.