Geodesic
Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 833-843

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The generalized k-connectivity κ_k (G) of a graph G was introduced by Hager in 1985. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized k-edge-connectivity which is defined as λ k(G) = min{λ (S) : S ⊆ V (G) and |S| = k }, where λ(S) denote the maximum number 𝓁 of pairwise edge-disjoint trees T_1, T_2, . . ., T_𝓁 in G such that S ⊆ V ( T_i ) for 1 ≤ i ≤𝓁. In this paper, we study the generalized edge- connectivity of product graphs and obtain sharp upper bounds for the generalized 3-edge-connectivity of Cartesian product graphs and strong product graphs. Among our results, some special cases are also discussed.
Keywords: generalized edge-connectivity, Cartesian product, strong product, lexicographic product 
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     title = {Sharp {Upper} {Bounds} for {Generalized} {Edge-Connectivity} of {Product} {Graphs}},
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Sun, Yuefang. Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 833-843. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a4/