2023/04/04 by Tingyan Ma, Ma, Tingyan, Ligong Wang +3
Chemistry · Computer Science · Mathematics · #05C09 #05C35 #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #G.2.2 #Graph theory and applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.2304.07093
openalex publication_date 2023/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V(G), E(G)) be a graph with vertex set V(G) and edge set E(G). For k≥2 and given any subset S⊆|V(G)| with |S|=k, if a graph G of order |V(G)|≥ k+1 always has a spanning tree T such that S is precisely the set of leaves of T, then the graph G is a k-leaf-connected graph. A graph G is called Hamilton-connected if any two vertices of G are connected by a Hamilton path. Based on the definitions of k-leaf-connected and Hamilton-connected, we known that a graph is 2-leaf-connected if and only if it is Hamilton-connected. During the past decades, there have been many results of sufficient conditions for Hamilton-connected with respect to topological indices. In this paper, we present sufficient conditions for a graph G to be k-leaf-connected in terms of the Zagreb index, the reciprocal degree distance or the hyper-Zagreb index. Furthermore, we use the first Zagreb index and hyper-Zagreb index of the complement graph G to give sufficient conditions for a graph G to be k-leaf-connected.