M. Aouchiche, G. Caporossi, and P. Hansen, Variable neighborhood search for extremal graphs

M. Aouchiche, G. Caporossi, P. Hansen, and M. Laffay, AutoGraphiX: a survey, Electronic Notes in Discrete Mathematics, vol.22, pp.515-520, 2005.
DOI : 10.1016/j.endm.2005.06.090

M. Aouchiche, G. Caporossi, P. Hansen, and C. Lucas, Variable neighborhood search for extremal graphs 28 : Autographix after fifteen years. Les Cahiers du GERAD, soumis pour publication, 2013.

M. Aouchiche, O. Favaron, and P. Hansen, Variable neighborhood search for extremal graphs. 22. Extending bounds for independence to upper irredundance, Discrete Applied Mathematics, vol.157, issue.17, pp.3497-3510, 2009.
DOI : 10.1016/j.dam.2009.04.004

M. Aouchiche and P. Hansen, Recherche ?? voisinage variable de graphes extr??maux??13. ?? propos de la maille, RAIRO - Operations Research, vol.39, issue.4, pp.275-293, 2005.
DOI : 10.1051/ro:2006006

M. Aouchiche-et-pierre-hansen-adrian-bondy, J. Fonlupt, J. Fouquet, J. Fournier, and . Jorgel, Automated results and conjectures on average distance in graphs Ramírez Alfonsín, ´ editeurs : Graph Theory in Paris, Trends in Mathematics, pp.21-36, 2007.

M. Aouchiche and P. Hansen, Nordhaus???Gaddum relations for proximity and remoteness in graphs, Computers & Mathematics with Applications, vol.59, issue.8, pp.2827-2835, 2010.
DOI : 10.1016/j.camwa.2010.02.001

M. Aouchiche and P. Hansen, Proximity and remoteness in graphs: Results and conjectures, Networks, vol.41, issue.2, pp.95-102, 2011.
DOI : 10.1002/net.20450

M. Aouchiche, P. Hansen, and C. Lucas, On the extremal values of the second largest Q-eigenvalue, Linear Algebra and its Applications, vol.435, issue.10, pp.2591-2606, 2011.
DOI : 10.1016/j.laa.2011.03.051

. Bibliographie, Variable neighborhood search for extremal graphs. 19. further conjectures and results about the randic index, MATCH Commun. Math. Comput. Chem, vol.58, pp.83-102, 2007.

M. Aouchiche, P. Hansen, and M. Zheng, Variable neighborhood search for extremal graphs 19. further conjectures and results about the randic index, MATCH Commun. Math. Comput. Chem, vol.58, pp.83-102, 2007.

F. Belardo, E. M. , L. Marzi, K. Slobodan, and . Simi´csimi´c, Some results on the index of unicyclic graphs. Linear algebra and its applications, pp.1048-1059, 2006.

C. Berge, Graphs and hypergraphs, 1973.

C. Bu and J. Zhou, Starlike trees whose maximum degree exceed 4

G. Caporossi, D. Cvetkovic, I. Gutman, and P. Hansen, Variable Neighborhood Search for Extremal Graphs. 2. Finding Graphs with Extremal Energy, Journal of Chemical Information and Computer Sciences, vol.39, issue.6, pp.984-996, 1999.
DOI : 10.1021/ci9801419

G. Caporossi, I. Gutman, and P. Hansen, Variable neighborhood search for extremal graphs, Computers & Chemistry, vol.23, issue.5, pp.469-477, 1999.
DOI : 10.1016/S0097-8485(99)00031-5

G. Caporossi and P. Hansen, Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system, Discrete Mathematics, vol.212, issue.1-2, pp.29-44, 2000.
DOI : 10.1016/S0012-365X(99)00206-X

G. Caporossi and P. Hansen, Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures, Discrete Mathematics, vol.276, issue.1-3, pp.81-94, 2004.
DOI : 10.1016/S0012-365X(03)00311-X

. Simi´csimi´c, A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph, Linear Algebra Appl, vol.429, pp.11-122770, 2008.

Y. Chen, Properties of spectra of graphs and line graphs, Appl. Math. J. Ser

R. K. Fan and . Chung, Spectral graph theory, de CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, 1997.

D. Cvetkovi´ccvetkovi´c, G. Simi´csimi´c, P. Caporossi, and . Hansen, Variable neighborhood search for extremal graphs 3 : On the largest eigenvalue of color-constrained trees. Linear and Multilinear Algebra, pp.143-160, 2001.

D. Cvetkovi´ccvetkovi´c, On graphs whose second largest eigenvalue does not exceed 1, pp.15-20, 1982.

D. Cvetkovi´ccvetkovi´c, New theorems for the signless Laplacian eigenvalues Bulletin des sciences mathématiques et naturelles, Académie des Sciences de Bucarest, vol.137, issue.33, pp.131-146, 2008.

D. Cvetkovi´ccvetkovi´c and I. Pevac, Man-machine theorem proving in graph theory, Artificial Intelligence, vol.35, issue.1, pp.1-23, 1988.
DOI : 10.1016/0004-3702(88)90030-6

D. Cvetkovi´ccvetkovi´c and P. Rowlinson, Spectra of unicyclic graphs. Graphs and combinatorics, pp.7-23, 1987.

D. Cvetkovi´ccvetkovi´c, P. Rowlinson, and K. Slobodan, Simi´cSimi´c : Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (Beograd), issue.95, pp.8111-8138, 2007.

D. Cvetkovi´ccvetkovi´c, P. Rowlinson, and K. Slobodan, Signless Laplacians of finite graphs, Linear Algebra and its Applications, vol.423, issue.1, pp.155-171, 2007.
DOI : 10.1016/j.laa.2007.01.009

D. Cvetkovi´ccvetkovi´c and K. Slobodan, On graphs whose second largest eigenvalue does not exceed (???5???1)2, 14th British Combinatorial Conference, pp.213-227, 1995.
DOI : 10.1016/0012-365X(94)00204-V

D. Cvetkovic and K. Slobodan, Simic : Towards a spectral theory of graphs based on the signless Laplacian, i. Publication de l, Institut Mathématique, issue.99, pp.8519-8552, 2009.

D. Cvetkovic and K. Slobodan, Simic : Towards a spectral theory of graphs based on the signless Laplacian, ii, Linear Algebra and its Applications, issue.9, p.432

D. Cvetkovic and K. Slobodan, Simic : Towards a spectral theory of graphs based on the signless laplacian, iii. Rapport technique, DOAJ-Articles, 2010.

M. Drago?, M. Cvetkovi´ccvetkovi´c, H. Doob, and . Sachs, Spectra of graphs, theory and applications, 1995.

K. Ch and . Das, On conjectures involving second largest signless Laplacian eigenvalue of graphs, Linear Algebra and its Applications, vol.432, issue.11, 2010.

K. Ch and . Das, Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs, Linear Algebra and its Applications, vol.435, issue.10, pp.2420-2424, 2011.

L. Silva-de-lima and V. Nikiforov, On the second largest eigenvalue of the signless Laplacian, Linear Algebra and its Applications, vol.438, issue.3, pp.1215-1222, 2013.
DOI : 10.1016/j.laa.2012.07.052

D. Ronald, . Dutton, C. Robert, F. Brigham, and . Gomez, Ingrid : A graph invariant manipulator, Journal of symbolic computation, vol.7, issue.2, pp.163-177, 1989.

R. D. Dutton, R. C. Brigham, and F. Gomez, INGRID: A graph invariant manipulator, Journal of Symbolic Computation, vol.7, issue.2, pp.163-177, 1989.
DOI : 10.1016/S0747-7171(89)80048-3

L. Susan and . Epstein, Learning and discovery : One system's search for mathematical knowledge, Computational Intelligence, vol.4, issue.1, pp.42-53, 1988.

Y. Fan, . Bit-shun, J. Tam, and . Zhou, Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order. Linear and Multilinear Algebra, pp.381-397, 2008.

Y. Fan, Y. Wang, and Y. Gao, Minimizing the least eigenvalues of unicyclic graphs with application to spectral spread, Linear Algebra and its Applications, vol.429, issue.2-3, pp.577-588, 2008.
DOI : 10.1016/j.laa.2008.03.012

Y. Fan, J. Xu, Y. Wang, and D. Liang, The Laplacian spread of a tree, Discrete Mathematics & Theoretical Computer Science, vol.10, issue.1, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00972305

Y. Fan and D. Yang, The Signless Laplacian Spectral Radius of Graphs with Given Number of Pendant Vertices, Graphs and Combinatorics, vol.25, issue.3, pp.291-298, 2009.
DOI : 10.1007/s00373-009-0840-1

L. Feng, Q. Li, and X. Zhang, Minimizing the Laplacian spectral radius of trees with given matching number. Linear and Multilinear Algebra, pp.199-207, 2007.

L. Feng and G. Yu, On three conjectures involving the signless Laplacian spectral radius of graph. Publications de l'Institut mathématique (Beograd) Nouvelle série On three conjectures involving the signless Laplacian spectral radius of graphs, Publ. Inst. Math. (Beograd), vol.8554, issue.9999, pp.35-38, 2009.

L. Feng and G. Yu, The Signless Laplacian Spectral Radius of Unicyclic Graphs with Graph Constraints, Kyungpook mathematical journal, vol.49, issue.1, pp.123-131, 2009.
DOI : 10.5666/KMJ.2009.49.1.123

M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J, vol.23, issue.98, pp.298-305, 1973.

E. Michael and . Fisher, On hearing the shape of a drum, Journal of Combinatorial Theory, vol.1, issue.1, pp.105-125, 1966.

F. R. Gantmacher, The theory of matrices, Vols, vol.1, issue.2

D. Gernert and L. Rabern, A knowledge-based system for graph theory, demonstrated by partial proofs for graph-colouring problems, MATCH Commun. Math. Comput. Chem, vol.58, issue.2, pp.445-460, 2007.

C. D. Godsil and B. D. Mckay, Constructing cospectral graphs. aequationes mathematicae, pp.257-268, 1982.

. H. Hs, H. Günthard, and . Primas, Zusammenhang von graphentheorie und motheorie von molekeln mit systemen konjugierter bindungen, Helvetica Chimica Acta, vol.39, issue.6, pp.1645-1653, 1956.

J. Guo, On the Laplacian spectral radius of a tree. Linear algebra and its applications, pp.379-385, 2003.

S. Guo, On bicyclic graphs whose second largest eigenvalue does not exceed 1, Linear Algebra and its Applications, vol.407, issue.0, pp.201-210, 2005.
DOI : 10.1016/j.laa.2005.05.010

I. Gutman, P. Hansen, and H. Mélot, Variable Neighborhood Search for Extremal Graphs. 10. Comparison of Irregularity Indices for Chemical Trees, Journal of Chemical Information and Modeling, vol.45, issue.2, pp.222-230, 2005.
DOI : 10.1021/ci0342775

W. H. Haemers, X. Liu, and Y. Zhang, Spectral characterizations of lollipop graphs, Linear Algebra and its Applications, vol.428, issue.11-12, pp.11-122415, 2008.
DOI : 10.1016/j.laa.2007.10.018

P. Hansen and C. Lucas, Bounds and conjectures for the signless Laplacien index of graphs, Les Cahiers du GERAD, 2009.

P. Hansen and C. Lucas, An inequality for the signless Laplacian index of a graph using the chromatic number. Graph Theory Notes of, pp.39-42, 2009.

P. Hansen and C. Lucas, Bounds and conjectures for the signless Laplacian index of graphs, Linear Algebra and its Applications, vol.432, issue.12, pp.3319-3336, 2010.
DOI : 10.1016/j.laa.2010.01.027

P. Hansen and H. Mélot, Variable Neighborhood Search for Extremal Graphs. 6. Analyzing Bounds for the Connectivity Index, Journal of Chemical Information and Computer Sciences, vol.43, issue.1, pp.1-14, 2003.
DOI : 10.1021/ci010133j

P. Hansen and N. Mladenovi´cmladenovi´c, Variable neighborhood search: Principles and applications, European Journal of Operational Research, vol.130, issue.3, pp.449-467, 2001.
DOI : 10.1016/S0377-2217(00)00100-4

P. Hansen, N. Mladenovi´cmladenovi´c, . José, and . Moreno-pérez, Variable neighbourhood search: methods and??applications, Annals of Operations Research, vol.60, issue.2, pp.367-407, 2010.
DOI : 10.1007/s10479-009-0657-6

P. Hansen and D. Stevanovi´cstevanovi´c, On bags and bugs, GRACO 2005,2nd Brazilian Symposium on Graphs, Algorithms and Combinatorics. [74] Bian He, Ya-Lei Jin et Xiao-Dong Zhang : Sharp bounds for the signless Laplacian spectral radius in terms of clique number. Linear Algebra and its Applications, pp.986-997, 2008.
DOI : 10.1016/j.dam.2007.05.044

C. He, J. Shao, and J. He, On the Laplacian spectral radii of bicyclic graphs, Discrete Mathematics, vol.308, issue.24, pp.5981-5995, 2008.
DOI : 10.1016/j.disc.2007.11.016

Y. Hong and X. Zhang, Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees, Discrete Mathematics, vol.296, issue.2-3, pp.187-197, 2005.
DOI : 10.1016/j.disc.2005.04.001

Y. Hou, Unicyclic graphs with minimal energy, Journal of Mathematical Chemistry, vol.29, issue.3, pp.163-168, 2001.
DOI : 10.1023/A:1010935321906

Y. Hou, I. Gutman, and C. Woo, Unicyclic graphs with maximal energy, Linear Algebra and its Applications, vol.356, issue.1-3, pp.27-36, 2002.
DOI : 10.1016/S0024-3795(01)00609-7

B. Huo, S. Ji, X. Li, and Y. Shi, Solution to a conjecture on the maximal energy of bipartite bicyclic graphs, Linear Algebra and its Applications, vol.435, issue.4, pp.804-810, 2011.
DOI : 10.1016/j.laa.2011.02.001

M. Kac, Can one hear the shape of a drum ? The american mathematical monthly, pp.1-23, 1966.

L. Yu, Kolotilina : Inequalities for the extreme eigenvalues of block-partitioned hermitian matrices with applications to spectral graph theory, Journal of Mathematical Sciences, vol.176, pp.44-56, 2011.

M. Lepovi´clepovi´c and I. Gutman, No starlike trees are cospectral. Discrete mathematics, pp.291-295, 2002.

J. Li and J. Shiu, On the second largest Laplacian eigenvalues of graphs, Linear Algebra and its Applications, vol.438, issue.5, pp.2438-2446, 2013.
DOI : 10.1016/j.laa.2012.10.047

X. Li and J. Zhang, On bicyclic graphs with maximal energy, Linear Algebra and its Applications, vol.427, issue.1, pp.87-98, 2007.
DOI : 10.1016/j.laa.2007.06.022

M. Liu and B. Liu, The signless Laplacian spread, Linear Algebra and its Applications, vol.432, issue.2-3, pp.505-514, 2010.
DOI : 10.1016/j.laa.2009.08.025

M. Liu, X. Tan, and B. Liu, The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices, Czechoslovak Mathematical Journal, vol.60, issue.3, pp.849-867, 2010.
DOI : 10.1007/s10587-010-0053-z

X. Liu, Y. Zhang, and X. Gui, The multi-fan graphs are determined by their Laplacian spectra, Discrete Mathematics, vol.308, issue.18, pp.4267-4271, 2008.
DOI : 10.1016/j.disc.2007.08.002

L. Lovász and J. Pelikan, On the eigenvalues of trees, Periodica Mathematica Hungarica, vol.175, issue.1-2, pp.175-182, 1973.
DOI : 10.1007/BF02018473

C. Lucas, Valeurs extrêmes du rayon spectral du Laplacien sans signe avec un invariant de distance fixé, 2013.

D. Brendan and . Mckay, On the spectral characterisation of trees, Ars Combin, vol.3, pp.219-232, 1977.

N. Mladenovi´cmladenovi´c and P. Hansen, Variable neighborhood search, Computers & Operations Research, vol.24, issue.11, pp.1097-1100, 1997.
DOI : 10.1016/S0305-0548(97)00031-2

T. Samuel-motzkin-et-ernst-gabor and . Straus, Maxima for graphs and a new proof of a theorem of turán, Canadian Journal of Mathematics, vol.17, pp.533-540, 1965.

C. Oliveira, L. S. Lima, N. M. Abreu, and P. Hansen, Bounds on the index of the signless Laplacian of a graph, Discrete Applied Mathematics, vol.158, issue.4, 2009.
DOI : 10.1016/j.dam.2009.06.023

G. R. Omidi and K. Tajbakhsh, Starlike trees are determined by their Laplacian spectrum, Linear Algebra and its Applications, vol.422, issue.2-3, pp.654-6581328, 2007.
DOI : 10.1016/j.laa.2006.11.028

M. Petrovi´cpetrovi´c and B. Mileki´cmileki´c, On the second largest eigenvalue of line graphs, Journal of Graph Theory, vol.27, issue.2, pp.61-66, 1998.
DOI : 10.1002/(SICI)1097-0118(199802)27:2<61::AID-JGT1>3.0.CO;2-D

J. R. Schott, Matrix analysis for statistics Wiley Series in Probability and Statistics, 2005.

A. J. Schwenk, Almost all trees are cospectral. In F. Harary, ´ editeur : New Directions in the Theory of Graphs, pp.275-307, 1973.

K. Slobodan and . Simi´csimi´c, On the largest eigenvalue of unicyclic graphs. Publications de l'Institut Mathématique, Nouvelle Série, vol.42, pp.13-19, 1987.

K. Slobodan and . Simi´csimi´c, On the largest eigenvalue of bicyclic graphs. Publications de l'Institut Mathématique, Nouvelle Série, vol.46, pp.1-6, 1989.

D. Stevanovi´cstevanovi´c, V. Brankov, D. Cvetkovi´ccvetkovi´c, and K. Slobodan, Simi´cSimi´c : New- Graph Available from <http, 2003.

G. Szekeres and S. Herbert, An inequality for the chromatic number of a graph, Journal of Combinatorial Theory, vol.4, issue.1, pp.1-3, 1968.
DOI : 10.1016/S0021-9800(68)80081-X

R. Edwin, . Van-dam, and H. Willem, Haemers : Which graphs are determined by their spectrum ?, Special issue on the Combinatorial Matrix Theory Conference (Pohang, pp.241-272, 2002.

J. Wang, F. Belardo, Q. Huang, and B. Bojana, On the two largest q-eigenvalues of graphs, Discrete Mathematics, issue.21, pp.3102858-2866, 2010.

P. Wocjan and C. Elphick, New spectral bounds on the chromatic number encompassing all eigenvalues of the adjacency matrix, 1209.

G. Xu, On unicyclic graphs whose second largest eigenvalue dose not exceed 1, Discrete Applied Mathematics, vol.136, issue.1, pp.117-124, 2004.
DOI : 10.1016/S0166-218X(03)00203-8

C. Yan, Properties of spectra of graphs and line graphs, Applied Mathematics-A Journal of Chinese Universities, vol.18, issue.2, pp.371-376, 2002.
DOI : 10.1007/s11766-002-0017-7

G. Yu, On the maximal signless Laplacian spectral radius of graphs with given matching number, Proc. Japan Acad, pp.163-166, 2008.
DOI : 10.3792/pjaa.84.163

J. Zhang and B. Zhou, On bicyclic graphs with minimal energies, Journal of Mathematical Chemistry, vol.64, issue.4, pp.423-431, 2005.
DOI : 10.1007/s10910-004-1108-x

X. Zhang, The signless Laplacian spectral radius of graphs with given degree sequences, Discrete Applied Mathematics, vol.157, issue.13, pp.2928-2937, 2009.
DOI : 10.1016/j.dam.2009.02.022

Y. Zhang, X. Liu, B. Zhang, and X. Yong, The lollipop graph is determined by its Q-spectrum, Discrete Mathematics, vol.309, issue.10, pp.3364-3369, 2009.
DOI : 10.1016/j.disc.2008.09.052