Hull numbers of Bicyclic and Tricyclic graphs

For two vertices u and v of a connected graph G, the set I[u, v] consists of all vertices lying on some u-v geodesic in G. Let S be a subset of the vertex set V(G), and denote by I[S] the union of all sets I[u, v] with u, v ∈ S. The set S is called convex if I[S] = S. The convex hull [S] of S is defined as the smallest convex set in G containing S. The hull number h(G) of a graph G is the cardinality of a smallest subset S ⊆ V(G) such that [S] = V(G). In this paper, we investigate the hull numbers of bicyclic and tricyclic graphs and provide a classification of these values.

کلیدواژه ها:

Hull number ، Bicyclic graphs ، Tricyclic graphs ، Extreme vertex