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 |
| _version_ | 1797713129958801408 |
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| author | Sun Yuefang |
| author_facet | Sun Yuefang |
| author_sort | Sun Yuefang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T07:32:27Z |
| format | Article |
| id | doaj.art-23a70569477644708c785bf83fbd9df7 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T07:32:27Z |
| publishDate | 2017-11-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-23a70569477644708c785bf83fbd9df72023-09-02T21:43:03ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922017-11-0137497598810.7151/dmgt.1982dmgt.1982A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product GraphsSun Yuefang0Department of Mathematics Shaoxing University, Zhejiang 312000, P.R. ChinaThe 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.https://doi.org/10.7151/dmgt.1982generalized connectivitygeneralized edge-connectivitystrong product. |
| spellingShingle | Sun Yuefang A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs Discussiones Mathematicae Graph Theory generalized connectivity generalized edge-connectivity strong product. |
| title | A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs |
| title_full | A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs |
| title_fullStr | A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs |
| title_full_unstemmed | A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs |
| title_short | A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs |
| title_sort | sharp lower bound for the generalized 3 edge connectivity of strong product graphs |
| topic | generalized connectivity generalized edge-connectivity strong product. |
| url | https://doi.org/10.7151/dmgt.1982 |
| work_keys_str_mv | AT sunyuefang asharplowerboundforthegeneralized3edgeconnectivityofstrongproductgraphs AT sunyuefang sharplowerboundforthegeneralized3edgeconnectivityofstrongproductgraphs |