Sharp bounds on the zeroth-order general Randić indices of conjugated bicyclic graphs

The zeroth-order general Randic index of a (molecular) graph G is defined as @?"v"@?"V"("G")(d(v))^@a, where d(v) is the degree of vertex v in G, and @a is an arbitrary real number. In this paper, we investigate the zeroth-order general Randic index of conjugated bicyclic graphs (i.e., bicyclic graphs with perfect matchings). We characterized the conjugated bicyclic graphs with maximum and minimum R"@a^0 according to @a in different intervals.

[1]  Shuchao Li,et al.  Sharp bounds for the Zagreb indices of bicyclic graphs with k-pendant vertices , 2010, Discret. Appl. Math..

[2]  L B Kier,et al.  Molecular connectivity. I: Relationship to nonspecific local anesthesia. , 1975, Journal of pharmaceutical sciences.

[3]  Béla Bollobás,et al.  Graphs of Extremal Weights , 1998, Ars Comb..

[4]  J. Gross,et al.  Graph Theory and Its Applications , 1998 .

[5]  Hongzhuan Wang,et al.  On zeroth-order general Randić index of conjugated unicyclic graphs , 2008 .

[6]  S. Unger.  Molecular Connectivity in Structure–activity Analysis , 1987 .

[7]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[8]  Shuchao Li,et al.  On the Maximum Zagreb Indices of Graphs with k Cut Vertices , 2010 .

[9]  Roberto Todeschini,et al.  Handbook of Molecular Descriptors , 2002 .

[10]  Shuchao Li,et al.  On the zeroth-order general Randić index , 2011 .

[11]  H. Deng,et al.  On Unicycle Graphs with Maximum and Minimum Zeroth-order Genenal Randić Index , 2007 .

[12]  Ivan Gutman,et al.  Chemical Graph Theory—The Mathematical Connection , 2006 .

[13]  Hanyuan Deng,et al.  Extremal (n,n + 1)-graphs with respected to zeroth- order general Randić index , 2007 .

[14]  N. Trinajstic.  Chemical Graph Theory , 1992 .

[15]  Xia Hu,et al.  On the Extremal Zagreb Indices of Graphs with Cut Edges , 2010 .

[16]  M. Randic.  Characterization of molecular branching , 1975 .

[17]  Xueliang Li,et al.  Connected (n, m)-graphs with minimum and maximum zeroth-order general Randic index , 2007, Discret. Appl. Math..

[18]  Béla Bollobás,et al.  Extremal graphs for weights , 1999, Discret. Math..

[19]  Yaoping Hou,et al.  Bounds on the largest eigenvalues of trees with a given size of matching , 2002 .

[20]  Shuchao Li,et al.  Sums of Powers of the Degrees of Graphs with k Cut Edges , 2011, Graphs Comb..

[21]  L. Hall,et al.  Molecular connectivity in chemistry and drug research , 1976 .

[22]  Carlos Uzcátegui,et al.  Randic ordering of chemical trees , 2005, Discret. Appl. Math..

[23]  Xueliang Li,et al.  A Survey on the Randic Index , 2008 .

[24]  Shuchao Li,et al.  On the maximum and minimum Zagreb indices of graphs with connectivity at most k , 2010, Appl. Math. Lett..

[25]  R. García-Domenech,et al.  Some new trends in chemical graph theory. , 2008, Chemical reviews.