Year: 2025
Type: article
Abstract: Let G be a simple graph. An isolating set of G is a set I of vertices such that removing I and its neighborhood leaves no edge. In addition, the set I is said to be an independent isolating set of G if I is an isolating set of G and G [ I ] has no edge, where G [ I ] represents the subgraph of G induced by I . The independent isolation number of G , denoted by ι i ( G ) , is the minimum cardinality of among all independent isolating sets of G . In this paper, we prove that for every tree T except a star, n ( T ) - | L ( T ) | - | S ( T ) | + 3 4 ≤ ι i ( T ) ≤ n ( T ) - | L ( T ) | + 2 | S ( T ) | 4 , where n ( T ) , L ( T ) and S ( T ) represent the order, the sets of leaves and support vertices, respectively. Finally, we characterize the extremal trees attaining the bounds.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.787
Authors: Quanli Hao, Xinhui An, Baoyindureng Wu
Institution: Xinjiang University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415369781