On the edge‐toughness of a graph. II
The edge‐toughness T1(G) of a graph G is defined as (Formula Presented.) where the minimum is taken over every edge‐cutset X that separates G into ω (G ‐ X) components. We determine this quantity for some special classes of graphs that also gives the arboricity of these graphs. We also give a simp...
| Main Authors: | , |
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| Format: | Article |
| Published: |
Wiley
1993
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| Online Access: | http://psasir.upm.edu.my/id/eprint/114944/ |
| _version_ | 1848866641596645376 |
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| author | Peng, Y.H. Tay, T.S. |
| author_facet | Peng, Y.H. Tay, T.S. |
| author_sort | Peng, Y.H. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The edge‐toughness T1(G) of a graph G is defined as (Formula Presented.) where the minimum is taken over every edge‐cutset X that separates G into ω (G ‐ X) components. We determine this quantity for some special classes of graphs that also gives the arboricity of these graphs. We also give a simpler proof to the following result of Peng et al.: For any positive integers r, s satisfying r/2 < s ≤ r, there exists an infinite family of graphs such that for each graph G in the family, λ(G) = r (where λ(G) is the edge‐connectivity of G) T1(G) = s, and G can be factored into s spanning trees. |
| first_indexed | 2025-11-15T14:23:50Z |
| format | Article |
| id | upm-114944 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:23:50Z |
| publishDate | 1993 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1149442025-02-12T07:13:42Z http://psasir.upm.edu.my/id/eprint/114944/ On the edge‐toughness of a graph. II Peng, Y.H. Tay, T.S. The edge‐toughness T1(G) of a graph G is defined as (Formula Presented.) where the minimum is taken over every edge‐cutset X that separates G into ω (G ‐ X) components. We determine this quantity for some special classes of graphs that also gives the arboricity of these graphs. We also give a simpler proof to the following result of Peng et al.: For any positive integers r, s satisfying r/2 < s ≤ r, there exists an infinite family of graphs such that for each graph G in the family, λ(G) = r (where λ(G) is the edge‐connectivity of G) T1(G) = s, and G can be factored into s spanning trees. Wiley 1993-06 Article PeerReviewed Peng, Y.H. and Tay, T.S. (1993) On the edge‐toughness of a graph. II. Journal of Graph Theory, 17 (2). pp. 233-246. ISSN 0364-9024; eISSN: 1097-0118 https://onlinelibrary.wiley.com/doi/10.1002/jgt.3190170211 10.1002/jgt.3190170211 |
| spellingShingle | Peng, Y.H. Tay, T.S. On the edge‐toughness of a graph. II |
| title | On the edge‐toughness of a graph. II |
| title_full | On the edge‐toughness of a graph. II |
| title_fullStr | On the edge‐toughness of a graph. II |
| title_full_unstemmed | On the edge‐toughness of a graph. II |
| title_short | On the edge‐toughness of a graph. II |
| title_sort | on the edge‐toughness of a graph. ii |
| url | http://psasir.upm.edu.my/id/eprint/114944/ http://psasir.upm.edu.my/id/eprint/114944/ http://psasir.upm.edu.my/id/eprint/114944/ |