# Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs

• Volume: 36, Issue: 4, page 833-843
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Yuefang Sun. "Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs." Discussiones Mathematicae Graph Theory 36.4 (2016): 833-843. <http://eudml.org/doc/287123>.

@article{YuefangSun2016,
abstract = {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.},
author = {Yuefang Sun},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {generalized edge-connectivity; Cartesian product; strong product; lexicographic product},
language = {eng},
number = {4},
pages = {833-843},
title = {Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs},
url = {http://eudml.org/doc/287123},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Yuefang Sun
TI - Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 4
SP - 833
EP - 843
AB - 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.
LA - eng
KW - generalized edge-connectivity; Cartesian product; strong product; lexicographic product
UR - http://eudml.org/doc/287123
ER -

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