Some Properties on Estrada Index of Folded Hypercubes Networks

Let be a simple graph with vertices and let be the eigenvalues of its adjacency matrix; the Estrada index of the graph is defined as the sum of the terms , . The -dimensional folded hypercube networks are an important and attractive variant of the -dimensional hypercube networks , which are obtained from by adding an edge between any pair of vertices complementary edges. In this paper, we establish the explicit formulae for calculating the Estrada index of the folded hypercubes networks by deducing the characteristic polynomial of the adjacency matrix in spectral graph theory. Moreover, some lower and upper bounds for the Estrada index of the folded hypercubes networks are proposed.

[1]  J. A. Rodríguez-Velázquez,et al.  Spectral measures of bipartivity in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Jianping Liu,et al.  Bounds of the Estrada index of graphs , 2010 .

[3]  Bo Zhou,et al.  Some Lower Bounds for Estrada Index , 2010 .

[4]  Shahram Latifi,et al.  Properties and Performance of Folded Hypercubes , 1991, IEEE Trans. Parallel Distributed Syst..

[5]  Hongmei Liu,et al.  Cycle Embedding in Faulty Folded Hypercube , 2013 .

[6]  Xie-Bin Chen,et al.  Construction of optimal independent spanning trees on folded hypercubes , 2013, Inf. Sci..

[7]  Jinde Cao,et al.  The Kirchhoff Index of Hypercubes and Related Complex Networks , 2013 .

[8]  M. Randic,et al.  On Characterization of 3D Molecular Structure , 2002 .

[9]  Bo Zhou,et al.  New upper bounds on Zagreb indices , 2009 .

[10]  Guanghui Wen,et al.  Consensus in multi‐agent systems with communication constraints , 2012 .

[11]  Hongmei Liu,et al.  On Constraint Fault-free Cycles in Folded Hypercube , 2013 .

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

[13]  Sheshayya A. Choudum,et al.  Embedding certain height-balanced trees and complete pm-ary trees into hypercubes , 2013, J. Discrete Algorithms.

[14]  Yilun Shang,et al.  LOWER BOUNDS FOR THE ESTRADA INDEX OF GRAPHS , 2012 .

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

[16]  Min Liu,et al.  Cycles embedding on folded hypercubes with vertex faults , 2013 .

[17]  Jirí Fink,et al.  Perfect matchings extend to Hamilton cycles in hypercubes , 2007, J. Comb. Theory, Ser. B.

[18]  Chen Ming,et al.  Spectrum of folded hypercubes , 2011 .

[19]  Xiaofeng Guo,et al.  Total chromatic number of folded hypercubes , 2013, Ars Comb..

[20]  D. Cvetkovic,et al.  Recent Results in the Theory of Graph Spectra , 2012 .

[21]  Jinde Cao,et al.  The Kirchhoff Index of Folded Hypercubes and Some Variant Networks , 2014 .

[22]  J. A. Rodríguez-Velázquez,et al.  Atomic branching in molecules , 2006 .