A majorization method for localizing graph topological indices

This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Using this method, we derive old and new bounds. Numerical examples are provided showing how current results in the literature could be improved.

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

[2]  Bo Zhou,et al.  A note on Kirchhoff index , 2008 .

[3]  P. Tarazaga.  More estimates for eigenvalues and singular values , 1991 .

[4]  I. Gutman,et al.  More on the Laplacian Estrada index , 2009 .

[5]  A. Chang,et al.  On the Laplacian Estrada index of a graph , 2009 .

[6]  Bo Zhou,et al.  On resistance-distance and Kirchhoff index , 2009 .

[7]  L. Lovász.  Combinatorial problems and exercises , 1979 .

[8]  Bo Zhou,et al.  On a novel connectivity index , 2009 .

[9]  Some localization theorems using a majorization technique , 2000 .

[10]  Bo Zhou.  On sum of powers of the Laplacian eigenvalues of graphs , 2008 .

[11]  I. Gutman.  The Energy of a Graph: Old and New Results , 2001 .

[12]  Bo Zhou,et al.  On the general sum-connectivity index of trees , 2011, Appl. Math. Lett..

[13]  Frank Harary,et al.  Graph Theory , 2016 .

[14]  D. Cvetkovic,et al.  Graph theory and molecular orbitals , 1974 .

[15]  Huiqing Liu,et al.  Some upper bounds for the energy of graphs , 2007 .

[16]  Anton Betten,et al.  Algebraic Combinatorics and Applications : Proceedings , 2001 .

[17]  Anna Torriero,et al.  Majorization under constraints and bounds of the second Zagreb index , 2011 .

[18]  R. Balakrishnan.  The energy of a graph , 2004 .

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

[20]  D. Alderson,et al.  Diversity of graphs with highly variable connectivity. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Rosanna Grassi,et al.  Extremal Properties of Graphs and Eigencentrality in Trees with a Given Degree Sequence , 2010 .

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

[23]  W. Haemers,et al.  A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo , 2008 .

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

[25]  I. Gutman,et al.  Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons , 1972 .

[26]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[27]  Vincent Moulton,et al.  Maximal Energy Graphs , 2001, Adv. Appl. Math..

[28]  T. Aushev,et al.  Radiative B meson decays into Kπγ and Kππγ final states , 2002 .

[29]  N. Trinajstic,et al.  The Zagreb Indices 30 Years After , 2003 .

[30]  Russell Merris,et al.  The Laplacian Spectrum of a Graph II , 1994, SIAM J. Discret. Math..

[31]  Jacobus H. Koolen,et al.  Maximal Energy Bipartite Graphs , 2003, Graphs Comb..

[32]  Bo Zhou.  ON SUM OF POWERS OF LAPLACIAN EIGENVALUES AND LAPLACIAN ESTRADA INDEX OF GRAPHS , 2009 .

[33]  I. Gutman,et al.  Graph theory and molecular orbitals. XII. Acyclic polyenes , 1975 .

[34]  Bolian Liu,et al.  A note on sum of powers of the Laplacian eigenvalues of graphs , 2011, Appl. Math. Lett..

[35]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .