The generalized k-connectivity κk(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 λk(G) = min{λ(S) : S ⊆ V (G) and |S| = k}, where λ(S) denote the maximum number ℓ of pairwise edge-disjoint trees T1, T2, . . . , Tℓ in G such that S ⊆ V (Ti) 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.
@article{bwmeta1.element.doi-10_7151_dmgt_1924,
author = {Yuefang Sun},
title = {Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {833-843},
zbl = {1350.05083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1924}
}
Yuefang Sun. Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 833-843. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1924/