| Issue |
RAIRO-Oper. Res.
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 3675 - 3688 | |
| DOI | https://doi.org/10.1051/ro/2022177 | |
| Published online | 31 October 2022 | |
Isolated toughness variant and fractional κ-factor
School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China
* Corresponding author: gaowei@ynnu.edu.cn
Received:
20
April
2022
Accepted:
4
October
2022
Isolated toughness is a crucial parameter considered in network security which characterizes the vulnerability of the network from the perspective of graph topology. I’(G) is the unique variant of isolated toughness which was introduced in 2001. This work investigates the correlation of I’(G) and the existence of fractional factor. It is proved that a graph G with δ(G) ≥ k admits fraction k-factor if I’(G) > 2k − 1, where k ≥ 2 is an integer. A counterexample is presented to show the sharpness of I’(G) bound.
Mathematics Subject Classification: 05C70
Key words: Graph / isolated toughness / fractional k-factor
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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