The atom-bond connectivity（ABC） index of a graph G, introduced by Estrada,Torres, Rodr′？guez and Gutman in 1998, is defined as the sum of the weights√1/di＋1/dj-2/didj of all edges vivj of G, where di denotes th...The atom-bond connectivity（ABC） index of a graph G, introduced by Estrada,Torres, Rodr′？guez and Gutman in 1998, is defined as the sum of the weights√1/di＋1/dj-2/didj of all edges vivj of G, where di denotes the degree of the vertex vi in G. In this paper, we give an upper bound of the ABC index of a two-tree G with n vertices, that is, ABC（G） ≤（2n- 4）√2/2＋√2n-4/n-1. We also determine the two-trees with the maximum and the second maximum ABC index.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.6116400561440005+6 种基金11161037)the Program for Changjiang Scholars and Innovative Research Team in Universities(Grant No.IRT-15R40)Key Laboratory of Tibetan Information Processing of Ministry of Education of Chinathe Research Fund for the Chunhui Program of Ministry of Education of China(Grant No.Z2014022)the Nature Science Foundation of Qinghai Province(Grant Nos.2013-Z-Y172014-ZJ-9072014-ZJ-721)
文摘The atom-bond connectivity（ABC） index of a graph G, introduced by Estrada,Torres, Rodr′？guez and Gutman in 1998, is defined as the sum of the weights√1/di＋1/dj-2/didj of all edges vivj of G, where di denotes the degree of the vertex vi in G. In this paper, we give an upper bound of the ABC index of a two-tree G with n vertices, that is, ABC（G） ≤（2n- 4）√2/2＋√2n-4/n-1. We also determine the two-trees with the maximum and the second maximum ABC index.
