Graphs with the maximal Estrada indices

Abstract Two new transformations are proposed to compare the Estrada indices between two graphs. Let Ψ n , m be the set of the ( n , m ) -graphs, where n and m are the numbers of vertices and edges, respectively. The graphs with the maximal Estrada indices in Ψ n , m are deduced by the new method for three cases, namely unicyclic and bipartite unicyclic graphs ( m = n ), bicyclic graphs ( m = n + 1 ), and the ( n , m ) -graphs without even cycles ( n + 1 ⩽ m ⩽ 3 ( n − 1 ) / 2 ).

[1]  Ivan Gutman,et al.  LOWER BOUNDS FOR ESTRADA INDEX , 2008 .

[2]  Bo Zhou,et al.  ON ESTRADA INDEX , 2008 .

[3]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Yi-Zheng Fan,et al.  Estrada Index of Random Graphs , 2012 .

[5]  Hanyuan Deng,et al.  A Proof of a Conjecture on the Estrada Index , 2009 .

[6]  Ernesto Estrada.  Characterization of the amino acid contribution to the folding degree of proteins , 2004, Proteins.

[7]  Dragan Stevanović,et al.  The Estrada index of chemical trees , 2009 .

[8]  Bo Zhou,et al.  The Estrada index of trees , 2011 .

[9]  Toufik Mansour,et al.  Relating Estrada index with spectral radius , 2007 .

[10]  Haixing Zhao,et al.  On the Estrada Index of Bipartite Graph 1 , 2009 .

[11]  Ivan Gutman,et al.  Lower bounds for Estrada index and Laplacian Estrada index , 2010, Appl. Math. Lett..

[12]  J. A. Peña,et al.  Estimating the Estrada index , 2007 .

[13]  D. Cvetkovic,et al.  Spectra of Graphs: Theory and Applications , 1997 .

[14]  Bo Zhou,et al.  On Estrada index of trees , 2011 .

[15]  New upper bounds for Estrada index of bipartite graphs , 2011 .

[16]  R. Balakrishnan,et al.  Skew spectra of graphs without even cycles , 2014 .

[17]  Yi-Zheng Fan,et al.  Maximum Estrada index of bicyclic graphs , 2012, Discret. Appl. Math..

[18]  Ernesto Estrada,et al.  Characterization of the folding degree of proteins , 2002, Bioinform..

[19]  Ernesto Estrada.  Characterization of 3D molecular structure , 2000 .

[20]  Zhibin Du,et al.  On the Estrada and Laplacian Estrada indices of graphs , 2011 .

[21]  Zhongxun Zhu,et al.  Tricyclic graph with maximal Estrada index , 2014, Discret. Appl. Math..

[22]  Bo Zhou,et al.  The Estrada index of unicyclic graphs , 2012 .

[23]  Bo Zhou,et al.  On the estrada index of graphs with given number of cut edges. , 2011 .

[24]  Amir Khosravanirad,et al.  A Lower Bound for Laplacian Estrada Index of a Graph , 2013 .

[25]  On the Laplacian Estrada Index of Unicyclic Graphs , 2012 .

[26]  Ernesto Estrada.  Topological structural classes of complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Bo Zhou,et al.  On maximum Estrada indices of graphs with given parameters , 2012 .

[28]  Zhibin Du,et al.  An edge grafting theorem on the Estrada index of graphs and its applications , 2013, Discret. Appl. Math..

[29]  Lusheng Wang,et al.  The Minimal Estrada Index of Trees with Two Maximum Degree Vertices , 2009 .