Author:
Cao Jingdong,Zhang Shumin,Ye Chengfu,Jia Tianxia
Abstract
Abstract
In the graph G = (V, E), V represents the set of vertices and E represents the set of edges. ℱ represents a family of graphs. A subset S ⊆ V is considered an ℱ -isolating set if G[V\NG[S]] does not contain F as a subgraph for all F ∈ ℱ. The ℱ-isolation number of the graph G, denoted by 𝜄(G, ℱ), is defined as the minimum cardinality of an ℱ-isolating set in G. If the family ℱ consists of a single graph H, then the subset S is referred to as an H-isolating set. The H-isolation number of the graph G, denoted by 𝜄
H
(G), is defined as the minimum cardinality of an H-isolating set in G. Maximal outerplanar graphs have been widely applied in different fields of research since 1891, where they hold significant importance. This paper aims to provide a comprehensive analysis of the H-isolation number in maximal outerplanar graphs,
ι
H
(
G
)
≤
min
{
n
2
k
+
4
,
n
+
n
2
2
k
+
5
,
n
−
n
2
2
k
+
2
}
, where H ≅ S
1,k+1,k+1.
Subject
Computer Science Applications,History,Education