The least eigenvalue of signless Laplacian of non-bipartite graphs with given domination number

Let G be a connected non-bipartite graph on n vertices with domination number @[email protected]?n+13. We present a lower bound for the least eigenvalue of the signless Laplacian of G in terms of the domination number.

[1]  Dragoš Cvetković,et al.  Towards a spectral theory of graphs based on the signless Laplacian, III , 2010 .

[2]  Yi-Zheng Fan,et al.  The least eigenvalues of the signless Laplacian of non-bipartite graphs with pendant vertices , 2013, Discret. Math..

[3]  F. Tian,et al.  Bounds of Laplacian spectrum of graphs based on the domination number , 2005 .

[4]  Guihai Yu,et al.  LAPLACIAN EIGENVALUES OF GRAPHS WITH GIVEN DOMINATION NUMBER , 2009 .

[5]  Shaun M. Fallat,et al.  Edge bipartiteness and signless Laplacian spread of graphs , 2012 .

[6]  Jinjiang Yuan,et al.  The least eigenvalue of the signless Laplacian of non-bipartite unicyclic graphs with k pendant vertices , 2013 .

[7]  Vladimir Nikiforov,et al.  The smallest eigenvalue of the signless Laplacian , 2011 .

[8]  C. Brand,et al.  Eigenvalues and domination in graphs , 1996 .

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

[10]  Yi-Zheng Fan,et al.  On edge singularity and eigenvectors of mixed graphs , 2008 .

[11]  Dragoš Cvetković,et al.  EIGENVALUE BOUNDS FOR THE SIGNLESS LAPLACIAN , 2007 .

[12]  Madhav Desai,et al.  A characterization of the smallest eigenvalue of a graph , 1994, J. Graph Theory.

[13]  Bao-Xuan Zhu.  The least eigenvalue of a graph with a given domination number , 2012 .

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

[15]  Guihai Yu,et al.  Minimizing the Laplacian eigenvalues for trees with given domination number , 2006 .

[16]  Min Zhou,et al.  A Sharp Upper Bound on the Least Signless Laplacian Eigenvalue Using Domination Number , 2014, Graphs Comb..

[17]  Cvetkovicccc Dragos,et al.  Towards a spectral theory of graphs based on the signless Laplacian, III , 2010 .

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

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

[20]  V. Nikiforov.  Bounds on graph eigenvalues I , 2006, math/0602027.

[21]  Yi-Zheng Fan,et al.  The least eigenvalue of signless Laplacian of graphs under perturbation , 2012 .

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

[23]  Yi-Zheng Fan,et al.  First eigenvalue and first eigenvectors of a nonsingular unicyclic mixed graph , 2009, Discret. Math..