Graphs with maximum Laplacian and signless Laplacian Estrada index

The Laplacian Estrada index ( L E E ) and the signless Laplacian Estrada index ( S L E E ) of a graph G are, respectively, the sum of the exponentials of the eigenvalues of the Laplacian and signless Laplacian matrix of G . The vertex frustration index ź b of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. Graphs having maximum L E E and S L E E values are determined among graphs with n vertices and 1 ź ź b ź n - 3 .

[1]  Ernesto Estrada,et al.  The Structure of Complex Networks: Theory and Applications , 2011 .

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

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

[4]  Jianping Li,et al.  Characterizing graphs with maximal Laplacian Estrada index , 2015 .

[5]  Qingying Deng,et al.  On extremal bipartite unicyclic graphs , 2014 .

[6]  Tomislav Doslic,et al.  Computing the bipartite edge frustration of fullerene graphs , 2007, Discret. Appl. Math..

[7]  D. Cvetkovic,et al.  Signless Laplacians of finite graphs , 2007 .

[8]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[9]  Dragoš Cvetković,et al.  A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph , 2008 .

[10]  Bo Zhou,et al.  LAPLACIAN ESTRADA INDEX OF TREES , 2011, 1106.3041.

[11]  O. Rojo,et al.  On the algebraic connectivity of some caterpillars: A sharp upper bound and a total ordering☆ , 2010 .

[12]  Ali Reza Ashrafi,et al.  Extremal properties of the bipartite vertex frustration of graphs , 2011, Appl. Math. Lett..

[13]  Juan A. Rodríguez-Velázquez,et al.  On a graph-spectrum-based structure descriptor , 2007 .

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

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

[16]  R. Merris.  A survey of graph laplacians , 1995 .

[17]  Ali Reza Ashrafi,et al.  Note on Estrada and $L$-Estrada indices of graphs , 2009 .

[18]  O. Rojo,et al.  EXTREMAL ALGEBRAIC CONNECTIVITIES OF CERTAIN CATERPILLAR CLASSES AND SYMMETRIC CATERPILLARS , 2010 .

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

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

[21]  Domingos M. Cardoso,et al.  Spectra of graphs obtained by a generalization of the join graph operation , 2013, Discret. Math..

[22]  Wai Chee Shiu,et al.  The normalized Laplacian Estrada index of a graph , 2014 .

[23]  V. Sunder,et al.  The Laplacian spectrum of a graph , 1990 .

[24]  M. Fiedler.  Eigenvalues of Nonnegative Symmetric Matrices , 1974 .

[25]  Ali Reza Ashrafi,et al.  The bipartite edge frustration of composite graphs , 2010, Discret. Appl. Math..

[26]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[27]  Yi-Zheng Fan,et al.  Bipartiteness and the least eigenvalue of signless Laplacian of graphs , 2012 .

[28]  Willem H. Haemers,et al.  Spectra of Graphs , 2011 .

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

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

[31]  Xiao-Dong Zhang,et al.  On the Laplacian eigenvalues of a graph , 1998 .

[32]  On matrices associated to directed graphs and applications , 2014 .

[33]  S. K. Ayyaswamy,et al.  Signless Laplacian Estrada Index , 2011 .

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

[35]  Wen-Huan Wang,et al.  Graphs with the maximal Estrada indices , 2014 .

[36]  D. Cvetkovic,et al.  Towards a spectral theory of graphs based on the signless Laplacian, I , 2009 .

[37]  N. Abreu.  Old and new results on algebraic connectivity of graphs , 2007 .

[38]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .