Abstract
The generalized k-connectivity κ k (G) of a graph G was introduced by Chartrand et al. in 1984. 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) denotes 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 prove that for any two connected graphs G and H we have λ 3(G □ H) ⩾ λ 3(G) + λ 3(H), where G □ H is the Cartesian product of G and H. Moreover, the bound is sharp. We also obtain the precise values for the generalized 3-edge-connectivity of the Cartesian product of some special graph classes.
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We acknowledge the support from National Natural Foundation of China through Project NSFC No. 11401389.
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Sun, Y. Generalized 3-edge-connectivity of Cartesian product graphs. Czech Math J 65, 107–117 (2015). https://doi.org/10.1007/s10587-015-0162-9
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DOI: https://doi.org/10.1007/s10587-015-0162-9