Extremal Graphs with Respect to the Zagreb Coindices

Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of graphs. In this paper we determine the extremal values of these new topological invariants over some special classes of graphs. The extremal graphs are also presented.

[1]  V. Nikiforov The sum of the squares of degrees: an overdue assignement , 2006, math/0608660.

[2]  R. Duffin Topology of series-parallel networks , 1965 .

[3]  Stephan G. Wagner,et al.  Some new results on distance-based graph invariants , 2009, Eur. J. Comb..

[4]  A. Kerber,et al.  SIMILARITY OF MOLECULAR DESCRIPTORS : THE EQUIVALENCE OF ZAGREB INDICES AND WALK COUNTS , 2004 .

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

[6]  Bo Zhou,et al.  On reciprocal molecular topological index , 2008 .

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

[8]  Danail Bonchev,et al.  Vertex-weightings for distance moments and thorny graphs , 2007, Discret. Appl. Math..

[9]  Kinkar Chandra Das,et al.  Maximizing the sum of the squares of the degrees of a graph , 2004, Discret. Math..

[10]  Dejan Plavšić,et al.  The distance matrix in chemistry , 1992 .

[11]  Ali Reza Ashrafi,et al.  The first and second Zagreb indices of some graph operations , 2009, Discret. Appl. Math..

[12]  Bo Zhou Upper bounds for the Zagreb indices and the spectral radius of series-parallel graphs , 2007 .

[13]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[14]  Bo Zhou,et al.  Relations between Wiener, hyper-Wiener and Zagreb indices , 2004 .

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

[17]  Dominique de Caen,et al.  An upper bound on the sum of squares of degrees in a graph , 1998, Discret. Math..

[18]  Alexandru I. Tomescu Unicyclic and bicyclic graphs having minimum degree distance , 2008, Discret. Appl. Math..