Double-Star Isolation of Maximal Outerplanar Graphs ∗

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, , where H ≅ S 1,k+1,k+1.