On Zagreb Indices and Coindices

A complete set of relations is established between the rst and second Zagreb index and coindex of a graph and of its complements. Formulas for the rst Zagreb index of several derived graphs are also obtained. A remarkable result is that the rst Zagreb coindices of a graph and of its complement are always equal.

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

[2]  Ali Reza Ashrafi,et al.  The Zagreb coindices of graph operations , 2010, Discret. Appl. Math..

[3]  Bo Zhou,et al.  Some properties of the reformulated Zagreb indices , 2010 .

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

[5]  Ante Graovac,et al.  On Vertex–Degree–Based Molecular Structure Descriptors , 2011 .

[6]  A. Ashrafi,et al.  Extermal properties of Zagreb coindices and degree distance of graphs , 2010 .

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

[8]  A. Ashrafi,et al.  More on Zagreb coindices of graphs , 2012 .

[9]  Hongbo Hua,et al.  More on Zagreb Coindices of Composite Graphs , 2012 .

[10]  Comparing Zagreb Indices and Coindices of Trees , 2012 .

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

[12]  Tomislav Doslic,et al.  Vertex-weighted Wiener polynomials for composite graphs , 2008, Ars Math. Contemp..

[13]  I. Gutman,et al.  A forgotten topological index , 2015, Journal of Mathematical Chemistry.

[14]  I. Gutman.  Degree-Based Topological Indices , 2013 .

[15]  Ivan Gutman,et al.  ON THE ORIGIN OF TWO DEGREE-BASED TOPOLOGICAL INDICES , 2014 .

[16]  I. Gutman,et al.  Testing the quality of molecular structure descriptors. Vertex-degree-based topological indices , 2013 .

[17]  Ivan Gutman,et al.  Zagreb indices of transformation graphs and total transformation graphs , 2014, Appl. Math. Comput..

[18]  Ali Reza Ashrafi,et al.  Extremal Graphs with Respect to the Zagreb Coindices , 2011 .

[19]  Hongbo Hua,et al.  Relations between Zagreb Coindices and Some Distance-Based Topological Indices ∗ , 2012 .

[20]  Matthias Dehmer,et al.  On structure-sensitivity of degree-based topological indices , 2013, Appl. Math. Comput..

[21]  ˇ TomislavDo,et al.  Vertex-Weighted Wiener Polynomials for Composite Graphs , 2008 .

[22]  Goran Popivoda,et al.  Chemical Trees with Extreme Values of Zagreb Indices and Coindices , 2014 .