Spectral radius and k-connectedness of a graph

A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted. In this paper, we present a tight sufficient condition for a connected graph with fixed minimum degree to be k-connected based on its spectral radius, for sufficiently large order.

[1]  Willem H. Haemers,et al.  Matchings in regular graphs from eigenvalues , 2009, J. Comb. Theory, Ser. B.

[2]  Binlong Li,et al.  Spectral radius and traceability of connected claw-free graphs , 2014, 1406.5404.

[3]  Xiao-Dong Zhang,et al.  On the Spectral Radius of Graphs with Cut Vertices , 2001, J. Comb. Theory, Ser. B.

[4]  Weijun Liu,et al.  Spectral conditions for some graphical properties , 2017 .

[5]  Vladimir Nikiforov,et al.  Some Inequalities for the Largest Eigenvalue of a Graph , 2002, Combinatorics, Probability and Computing.

[6]  F. Tian,et al.  Edge-connectivity and (signless) Laplacian eigenvalue of graphs , 2013 .

[7]  Huiqing Liu,et al.  Spectral radius and Hamiltonian graphs , 2012 .

[8]  Douglas R. Woodall,et al.  Best Monotone Degree Conditions for Graph Properties: A Survey , 2015, Graphs Comb..

[9]  John Adrian Bondy,et al.  A method in graph theory , 1976, Discret. Math..

[10]  Binlong Li,et al.  Spectral analogues of Moon–Moser's theorem on Hamilton paths in bipartite graphs , 2017 .

[11]  Vladimir Nikiforov,et al.  The spectral radius of graphs without paths and cycles of specified length , 2009, 0903.5351.

[12]  P. Hansen,et al.  On the spectral radius of graphs with a given domination number , 2007 .

[13]  Yuan Hong,et al.  A Sharp Upper Bound of the Spectral Radius of Graphs , 2001, J. Comb. Theory, Ser. B.

[14]  B. Bollobás,et al.  Extremal Graph Theory , 2013 .

[15]  Sebastian M. Cioabă,et al.  Eigenvalues and edge-connectivity of regular graphs , 2010 .

[16]  Ruifang Liu,et al.  Sufficient spectral conditions on Hamiltonian and traceable graphs , 2014, 1412.5273.

[17]  Sebastian M. Cioaba,et al.  Edge-Connectivity, Eigenvalues, and Matchings in Regular Graphs , 2010, SIAM J. Discret. Math..

[18]  Vladimir Nikiforov,et al.  Spectral radius and Hamiltonicity of graphs , 2009, 0903.5353.

[19]  Bo Ning,et al.  Spectral radius and Hamiltonian properties of graphs , 2013, 1309.0217.

[20]  Hong-Jian Lai,et al.  Edge‐Disjoint Spanning Trees, Edge Connectivity, and Eigenvalues in Graphs , 2016, J. Graph Theory.

[21]  Richard A. Brualdi,et al.  On the spectral radius of complementary acyclic matrices of zeros and ones , 1986 .

[22]  V. Chvátal.  On Hamilton's ideals , 1972 .

[23]  Weijun Liu,et al.  The spectral radius of edge chromatic critical graphs , 2016 .

[24]  L. Sunil Chandran,et al.  Minimum cuts, girth and a spectral threshold , 2004, Inf. Process. Lett..

[25]  David A. Gregory,et al.  Large matchings from eigenvalues , 2007 .

[26]  Vladimir Nikiforov,et al.  Spectral radius and Hamiltonicity of graphs with large minimum degree , 2016, Czechoslovak Mathematical Journal.

[27]  Xiaofeng Gu,et al.  Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs , 2016, ArXiv.

[28]  Dragan Stevanović.  Spectral Radius of Graphs , 2014 .

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