The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,...The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,where du denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4.In this paper,we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.展开更多
Another version of atom-bond connectivity index was defined by Graovac and Ghorbani, and called the second atom-bond connectivity index(ABC_2), which can provide convenience for molecular feature and its extreme value...Another version of atom-bond connectivity index was defined by Graovac and Ghorbani, and called the second atom-bond connectivity index(ABC_2), which can provide convenience for molecular feature and its extreme values are the focus of study. In this paper, by fractional comparison, we give the structural properties of the extremal graphs which attain the minimal ABC_2 index of unicyclic graphs of order n.展开更多
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(11071272,10831001,11171279,11101087)the Young Talent Foundation of Fuzhou University(XRC-1154)
文摘The atom-bond connectivity（ABC） index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G） =∑ uv∈E（G） √d u＋dv-2 dudv,where du denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4.In this paper,we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.
文摘Another version of atom-bond connectivity index was defined by Graovac and Ghorbani, and called the second atom-bond connectivity index(ABC_2), which can provide convenience for molecular feature and its extreme values are the focus of study. In this paper, by fractional comparison, we give the structural properties of the extremal graphs which attain the minimal ABC_2 index of unicyclic graphs of order n.
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.
