A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs
The generalized k-connectivity κk(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 λk(G...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2017-11-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1982 |
| Summary: | The generalized k-connectivity κk(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 λk(G) = min{λG(S) | S ⊆ V (G) and |S| = k}, where λG(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 get a sharp lower bound for the generalized 3-edge-connectivity of the strong product of any two connected graphs. |
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| ISSN: | 2083-5892 |