A special class of triple starlike trees characterized by Laplacian spectrum

Two graphs are said to be cospectral with respect to the Laplacian matrix if they have the same Laplacian spectrum. A graph is said to be determined by the Laplacian spectrum if there is no other non-isomorphic graph with the same Laplacian spectrum. In this paper, we prove that one special class of triple starlike tree is determined by its Laplacian spectrum.

[1]  A. Kelmans,et al.  A certain polynomial of a graph and graphs with an extremal number of trees , 1974 .

[2]  Q. Huang,et al.  Signless Laplacian spectral characterization of 4-rose graphs , 2016 .

[3]  Hai-Ying Shan,et al.  The spectral characterization of butterfly-like graphs , 2017 .

[4]  Xiaogang Liu,et al.  The lollipop graph is determined by its Q-spectrum , 2009, Discret. Math..

[5]  Changjiang Bu,et al.  Starlike trees whose maximum degree exceed 4 are determined by their Q-spectra , 2012 .

[6]  Q. Huang,et al.  Laplacian spectral characterization of 3-rose graphs , 2013 .

[7]  Behruz Tayfeh-Rezaie,et al.  Spectral characterization of graphs with index at most 2+5 , 2007 .

[8]  Bo Zhou,et al.  On Laplacian Eigenvalues of a Graph , 2004 .

[9]  Dariush Kiani,et al.  THE SUN GRAPH IS DETERMINED BY ITS SIGNLESS LAPLACIAN SPECTRUM , 2010 .

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

[11]  Yuanping Zhang,et al.  Determination of double quasi-star tree from its Laplacian spectrum , 2010 .

[12]  Changjiang Bu,et al.  Signless Laplacian spectral characterization of the cones over some regular graphs , 2012 .

[13]  Wei Wang,et al.  Note: The T-shape tree is determined by its Laplacian spectrum , 2006 .

[14]  Yuanping Zhang,et al.  Graph Zn and some graphs related to Zn are determined by their spectrum , 2005 .

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

[16]  Nair Maria Maia de Abreu,et al.  The characteristic polynomial of the Laplacian of graphs in (a,b)-linear classes , 2002 .

[17]  Xiaogang Liu,et al.  Laplacian spectral characterization of some double starlike trees , 2012, 1205.6027.

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

[19]  Mirko Lepovic,et al.  The high-energy band in the photoelectron spectrum of alkanes and its dependence on molecular structure , 1999 .

[20]  Willem H. Haemers,et al.  Developments on Spectral Characterizations of Graphs , 2007, Discret. Math..

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

[22]  H. Günthard,et al.  Zusammenhang von Graphentheorie und MO-Theorie von Molekeln mit Systemen konjugierter Bindungen , 1956 .

[23]  Q. Huang,et al.  On the Laplacian spectral characterization of Π-shape trees , 2018, Indian Journal of Pure and Applied Mathematics.

[24]  Sezer Sorgun,et al.  On the spectral characterization of kite graphs , 2015, 1506.01632.

[25]  K. Tajbakhsh,et al.  Starlike trees are determined by their Laplacian spectrum , 2007 .

[26]  Xiaogang Liu,et al.  One special double starlike graph is determined by its Laplacian spectrum , 2009, Appl. Math. Lett..