Laplacian Spectral Characterization of Some Unicyclic Graphs

Let be the unicyclic graph with vertices obtained by attaching two paths of lengths and at two adjacent vertices of cycle . Let be the unicyclic graph with vertices obtained by attaching paths of lengths at the same vertex of cycle . In this paper, we prove that and are determined by their Laplacian spectra when is even.

[1]  Bolian Liu,et al.  Graphs determined by their (signless) Laplacian spectra , 2011 .

[2]  Muhuo Liu.  Some graphs determined by their (signless) Laplacian spectra , 2012 .

[3]  Yaoping Hou,et al.  A class of unicyclic graphs determined by their Laplacian spectrum , 2012 .

[4]  Jianfeng Wang,et al.  Spectral Characterizations of Dumbbell Graphs , 2010, Electron. J. Comb..

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

[6]  W. Haemers,et al.  Which graphs are determined by their spectrum , 2003 .

[7]  Changjiang Bu,et al.  Spectral Characterizations of the Corona of a Cycle and Two Isolated Vertices , 2014, Graphs Comb..

[8]  Bolian Liu,et al.  Some results on the Laplacian spectrum , 2010, Comput. Math. Appl..

[9]  Yuanping Zhang,et al.  Spectral characterizations of lollipop graphs , 2008 .

[10]  Romain Boulet.  The centipede is determined by its Laplacian spectrum , 2008 .

[11]  Xiaogang Liu,et al.  Laplacian spectral characterization of some graph products , 2010, 1007.2472.

[12]  Xiaogang Liu,et al.  On the spectral characterization of some unicyclic graphs , 2011, Discret. Math..

[13]  Haixing Zhao,et al.  Spectral characterization of multicone graphs , 2012 .

[14]  Heping Zhang,et al.  Some graphs determined by their spectra , 2009 .

[15]  Yong-Liang Pan,et al.  A note on the second largest eigenvalue of the laplacian matrix of a graph , 2000 .

[16]  Bertrand Jouve,et al.  The Lollipop Graph is Determined by its Spectrum , 2008, Electron. J. Comb..

[17]  Romain Boulet.  Spectral characterizations of sun graphs and broken sun graphs , 2009, Discret. Math. Theor. Comput. Sci..

[18]  Changjiang Bu,et al.  Laplacian spectral characterization of some graphs obtained by product operation , 2012, Discret. Math..

[19]  Dragos Cvetkovic,et al.  An Introduction to the Theory of Graph Spectra: Frontmatter , 2009 .

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

[21]  STARLIKE TREES WITH MAXIMUM DEGREE 4 ARE DETERMINED BY THEIR SIGNLESS LAPLACIAN SPECTRA , 2010 .