On the signless Laplacian spectral radius of some graphs

doi:10.3969/j.issn.1000-5641.2017.01.004

Abstract

Abstract:

Let A(G) be the adjacent matrix of G and Q(G) = D(G)+A(G) is the signless Laplacian matrix of G. The signless Laplacian spectral radius of G is the largest eigenvalue of Q(G). In this paper we characterize the graphs with the maximum signless Laplacian spectral radii among the graphs with given vertex connectivity, among the graphs with given number of blocks and among the graphs with given pendant vertices, respectively.

Key words: signless Laplacian spectral radius, vertex connectivity, block, pendant vertex

CHEN Yuan-yuan, MU Shan-zhi, WANG Guo-ping. On the signless Laplacian spectral radius of some graphs[J]. Journal of East China Normal University(Natural Sc, doi: 10.3969/j.issn.1000-5641.2017.01.004.

References

[ 1 ] ZHANG X. The Laplacian spectral radius of some bipartite graphs[J]. Linear Algebra Appl, 2008, 428: 1610-1619.
[ 2 ] LI J, SHIU W, CHAN W. On the Laplacians spectral radius of bipartite graphs[J]. Linear Algebra Appl, 2011,435: 2183-2192.
[ 3 ] ABREU N, CARDOSO D. On the Laplacian and signless Laplacian spectrum of graph with k pairwise co-neighbor vertices[J]. Linear Algebra Appl, 2012, 437: 2308-2316.
[ 4 ] NING W, LI H. On the signless Laplacians spectral radius of irregular graphs[J]. Linear Algebra Appl, 2013,438: 2280-2288.
[ 5 ] CAI G, FAN Y. The signless Laplacians spectral radius of graphs with chromatic number[J]. Math Appl, 2009,22: 161-167.
[ 6 ] CVETKOVICL D, SIMIC S K. Towards a spectral theory of graphs based on signless Laplacian II[J]. Linear Algebra Appl, 2010, 432: 2257-2272.
[ 7 ] LIU H, LU M. On the spectral radius of graphs with cut edges[J]. Linear Algebra Appl, 2004, 389: 139-145.
[ 8 ] LIU M, LIU B L. The signless Laplacian spread[J]. Linear Algebra Appl, 2010, 432(2-3): 505-514.
[ 9 ] WANG J, HUANG Q. Some results on the signless Laplacians of graphs[J]. Applied Mathematics Letters, 2010,23: 1045-1049.
[10] ZHANG M, LI S. On the signless Laplacian spectra of k-trees[J]. Linear Algebra Appl, 2015, 467: 136-148.
[11] LI J, SHIU W, CHAN W. The Laplacians spectral radius of some grapgs[J]. Linear Algebra Appl, 2009, 431: 99-103.
[12] LIU M. The (signless) Laplacian spectral radius of c-cyclic graphs with n vertices and k pendant vertices[J].Electronic Journal of Linear Algebra, 2012, 23: 945-952.
[13] YE M, FAN Y Z. Maximizing signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity[J]. Linear Algebra Appl, 2010, 433: 1180-1186.
[14] WANG J F, HUANG Q X. Maximizing the signless Laplacians spectral radius of graphs with given diameter or cut vertices[J]. Linear and Multilinear Algebra, 2011, 59(7): 733-744.
[15] BERMAN A, ZHANG X D. On the spectral radius of graphs with cut vertices[J]. Journal of Combinatorial Theory, Series B, 2001, 83: 233-243.
[16] WU B F, XIAO E. The spectral radius of trees on k pendant vertices[J]. Linear Algebra Appl, 2005, 395: 343-349.
[17] LIN H Q, YANGW. Distance spectral radius of digraphs with given connectivity[J]. Discrete Mathematics, 2012,312: 1849-1856.
[18] CVETKOVIC D, ROWLINSON P, SIMIC S K. Signless Laplacian of finite graphs[J]. Linear Algebra Appl, 2007,423: 155-171.
[19] HONG Y, ZHANG X D. Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees [J]. Discrete Mathematics, 2005, 296: 187-197.

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