On generalized 3-connectivity of the strong product of graphs
Copyright policy )On generalized 3-connectivity of the strong product of graphs
Let G be a connected graph with n vertices and let k be an integer such that 2 ? k ? n. The generalized connectivity kk(G) of G is the greatest positive integer l for which G contains at least l internally disjoint trees connecting S for any set S ? V (G) of k vertices. We focus on the generalized connectivity of the strong product G1 _ G2 of connected graphs G1 and G2 with at least three vertices and girth at least five, and we prove the sharp bound k3(G1 _ G2) ? k3(G1)_3(G2) + k3(G1) + k3(G2)-1.
- University of Seville Spain
generalized connectivity, Connectivity, Whitney's theorem, tree-connectivity, Graph Theory, connectivity, Menger's theorem, Graph operations (line graphs, products, etc.), vertex connectivity, strong product graphs
generalized connectivity, Connectivity, Whitney's theorem, tree-connectivity, Graph Theory, connectivity, Menger's theorem, Graph operations (line graphs, products, etc.), vertex connectivity, strong product graphs
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