Citation
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
Abstract
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.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.1016/0012-365X(93)90147-L |
| Keywords: | Edge toughness; Order; Size; Minimum degree; Path number; Spanning forest; Balanced graph. |
| Depositing User: | Ms. Azian Edawati Zakaria |
| Date Deposited: | 03 Feb 2025 07:19 |
| Last Modified: | 03 Feb 2025 07:19 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1016/0012-365X(93)90147-L |
| URI: | http://psasir.upm.edu.my/id/eprint/114824 |
| Statistic Details: | View Download Statistic |
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