Geodesic
A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 4, pp. 975-988

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The generalized k-connectivity κ_k (G) of a graph G, mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity. 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_G (S) | S ⊆ V (G) and |S| = k }, where λ_G (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 get a sharp lower bound for the generalized 3-edge-connectivity of the strong product of any two connected graphs.
Keywords: generalized connectivity, generalized edge-connectivity, strong product 
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     author = {Sun, Yuefang},
     title = {A {Sharp} {Lower} {Bound} {For} {The} {Generalized} {3-Edge-Connectivity} {Of} {Strong} {Product} {Graphs}},
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Sun, Yuefang. A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 4, pp. 975-988. http://geodesic.mathdoc.fr/item/DMGT_2017_37_4_a8/