On the higher-order edge toughness of a graph
For an integer c, 1≤c≤{curly logical or}V(G){curly logical or}-1, we define the cth-order edge toughness of a graph G as tc(G)=min |X| ω(G-X)-cX⊆E(G) & ω(G-X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughne...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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1993
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| Online Access: | http://psasir.upm.edu.my/id/eprint/114824/ http://psasir.upm.edu.my/id/eprint/114824/1/114824.pdf |
| _version_ | 1848866606043627520 |
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| author | Chen, C.C. Koh, K.M. Peng, Y.H. |
| author_facet | Chen, C.C. Koh, K.M. Peng, Y.H. |
| author_sort | Chen, C.C. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | For an integer c, 1≤c≤{curly logical or}V(G){curly logical or}-1, we define the cth-order edge toughness of a graph G as tc(G)=min |X| ω(G-X)-cX⊆E(G) & ω(G-X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughness τc(G) of a graph G, we prove that 'τc(G)≥k if and only if G has k edge-disjoint spanning forests with exactly c components'. We also study the 'balancity' of a graph G of order p and size q, which is defined as the smallest positive integer c such that τc(G) = p/(p-c). © 1993. |
| first_indexed | 2025-11-15T14:23:16Z |
| format | Article |
| id | upm-114824 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:23:16Z |
| publishDate | 1993 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1148242025-02-03T07:19:14Z http://psasir.upm.edu.my/id/eprint/114824/ On the higher-order edge toughness of a graph Chen, C.C. Koh, K.M. Peng, Y.H. For an integer c, 1≤c≤{curly logical or}V(G){curly logical or}-1, we define the cth-order edge toughness of a graph G as tc(G)=min |X| ω(G-X)-cX⊆E(G) & ω(G-X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughness τc(G) of a graph G, we prove that 'τc(G)≥k if and only if G has k edge-disjoint spanning forests with exactly c components'. We also study the 'balancity' of a graph G of order p and size q, which is defined as the smallest positive integer c such that τc(G) = p/(p-c). © 1993. 1993 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/114824/1/114824.pdf Chen, C.C. and Koh, K.M. and Peng, Y.H. (1993) On the higher-order edge toughness of a graph. Discrete Mathematics, 111 (1-3). pp. 113-123. ISSN 0012-365X; eISSN: 0012-365X https://linkinghub.elsevier.com/retrieve/pii/0012365X9390147L 10.1016/0012-365X(93)90147-L |
| spellingShingle | Chen, C.C. Koh, K.M. Peng, Y.H. On the higher-order edge toughness of a graph |
| title | On the higher-order edge toughness of a graph |
| title_full | On the higher-order edge toughness of a graph |
| title_fullStr | On the higher-order edge toughness of a graph |
| title_full_unstemmed | On the higher-order edge toughness of a graph |
| title_short | On the higher-order edge toughness of a graph |
| title_sort | on the higher-order edge toughness of a graph |
| url | http://psasir.upm.edu.my/id/eprint/114824/ http://psasir.upm.edu.my/id/eprint/114824/ http://psasir.upm.edu.my/id/eprint/114824/ http://psasir.upm.edu.my/id/eprint/114824/1/114824.pdf |