Issue |
RAIRO-Oper. Res.
Volume 58, Number 5, September-October 2024
|
|
---|---|---|
Page(s) | 4607 - 4619 | |
DOI | https://doi.org/10.1051/ro/2024178 | |
Published online | 24 October 2024 |
A note on the P3-isolation number of a graph
1
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P.R. China
2
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P.R. China
* Corresponding author: gzh_ang@163.com
Received:
17
December
2023
Accepted:
11
September
2024
For any graph G, a subset D ⊆ V (G) is called a P3-isolating set of G if G − N[D] contains no P3 as a subgraph, that is, consists of isolated vertices and isolated edges only. The P3-isolation number of G, denoted by ι(G, P3), is the cardinality of a smallest P3-isolating set of G. Zhang and Wu [Discrete Appl. Math. 304 (2021) 365–374] investigated the parameter ι(G, P3) of a graph, and they proved that if G ∉ {P3, C3, C6} is a connected graph of order n, then ι(G,P3)≤27n. In this paper, we shall prove that if G ∉ {P3, C7, C11} is a connected graph of order n without triangles and induced 6-cycles, then ι(G,P3)≤n4, and the upper bound is sharp. This extends a result on ι(T, P3) of a tree T by Caro and Hansberg [Filomat 31 (2017) 3925–3944].
Mathematics Subject Classification: 05C69
Key words: Isolation number / partial domination / induced 6-cycles / triangle-free
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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