树型结构分子图的两类Zagreb指标（英文）
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摘要
图G的第三Zagreb指标和第三版Zagreb指标分别是M3(G)=∑uv∈E(G)|d(u)-d(v)|,M′1(G)=∑u∈V(G)dG(u)δG(u).该文研究了树型结构分子图的两类Zagreb指标.更准确地说,得到了一个随机选择的树型结构的n阶分子图的两类Zagreb指标的平均值和方差的界.
The third Zagreb index and the third version of Zagreb indices of a graph G are M3(G)=∑uv∈E(G)|d(u)-d(v)| and M′1(G)=∑u∈V(G)dG(u)δG(u) respectively.In this paper,we study the two Zagreb indices of molecular graph with tree structure.More precisely,we obtain the bounds for the average and variance of two indices in a randomly chosen molecular graph with tree structure of order n.
The third Zagreb index and the third version of Zagreb indices of a graph G are M3(G)=∑uv∈E(G)|d(u)-d(v)| and M′1(G)=∑u∈V(G)dG(u)δG(u) respectively.In this paper,we study the two Zagreb indices of molecular graph with tree structure.More precisely,we obtain the bounds for the average and variance of two indices in a randomly chosen molecular graph with tree structure of order n.
引文
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[3]Ghorbani M,Hosseinzadeh M.A new version of Zagreb indices[J].Filomat,2012,1(1):93-100.
[4]Ghorbani M,Hosseinzadeh M.The third version of Zagreb index[J].Discrete Math Algorithms and Applications,2013,5(4).
[5]Kazemi R.Note on the multiplicative Zagreb indices[J].Discrete Appl Math,2016,198:147-154.
[6]Kazemi R.Probabilistic analysis of the first Zagreb index[J].Trans Comb,2013,2(2):35-40.
[7]Kazemi R.The eccentric connectivity index of bucket recursive trees[J].Iranian J Math Chem,2014,5:77-83.
[8]Balaban A.T,Motoc I,Bondchev D,et al.Topological indices for structure-activity correlations[J].Topics Curr Chem,1983,114:21-55.
[9]Billingsley P.Probability and Measure[M].New York,Wiley,1885.
[10]Kazemi R.The second Zagreb index of molecular graphs with tree structure[J].MATCH Commun Math Comput Chem,2014,72(3):753-760.
[11]Lin H.On Segments,Vertices of degree two and the first Zagreb index of trees[J].MATCH Commun Math Comput Chem,2014,72(3):603-616.
[12]Todeschini R,Consonni V.Handbook of Molecular Descriptors[M].Wiley-VCH Weinheim,2000.
[13]Zhou B,Trinajsti N.Some properties of the reformulated Zagreb indices[J].J Math Chem,2010,48(3):714-719.
[2]Gutman I,Das K C.The first Zagreb indices 30years after[J].MATCH Commun Math Chem,2004,50:83-92.
[3]Ghorbani M,Hosseinzadeh M.A new version of Zagreb indices[J].Filomat,2012,1(1):93-100.
[4]Ghorbani M,Hosseinzadeh M.The third version of Zagreb index[J].Discrete Math Algorithms and Applications,2013,5(4).
[5]Kazemi R.Note on the multiplicative Zagreb indices[J].Discrete Appl Math,2016,198:147-154.
[6]Kazemi R.Probabilistic analysis of the first Zagreb index[J].Trans Comb,2013,2(2):35-40.
[7]Kazemi R.The eccentric connectivity index of bucket recursive trees[J].Iranian J Math Chem,2014,5:77-83.
[8]Balaban A.T,Motoc I,Bondchev D,et al.Topological indices for structure-activity correlations[J].Topics Curr Chem,1983,114:21-55.
[9]Billingsley P.Probability and Measure[M].New York,Wiley,1885.
[10]Kazemi R.The second Zagreb index of molecular graphs with tree structure[J].MATCH Commun Math Comput Chem,2014,72(3):753-760.
[11]Lin H.On Segments,Vertices of degree two and the first Zagreb index of trees[J].MATCH Commun Math Comput Chem,2014,72(3):603-616.
[12]Todeschini R,Consonni V.Handbook of Molecular Descriptors[M].Wiley-VCH Weinheim,2000.
[13]Zhou B,Trinajsti N.Some properties of the reformulated Zagreb indices[J].J Math Chem,2010,48(3):714-719.