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Algebraic conditions for $t$-tough graphs
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1079-1089 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We give some algebraic conditions for $t$-tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.
We give some algebraic conditions for $t$-tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.
Classification : 05C50, 05C75, 15A18
Keywords: $t$-tough graph; Laplacian matrix; adjacent matrix; eigenvalues 
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Liu, BoLian; Chen, Siyuan. Algebraic conditions for $t$-tough graphs. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1079-1089. http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a16/

[1] Brouwer, A. E.: Toughness and spectrum of a graph. Linear Algebra Appl. 226-228 (1995), 267-271. | MR | Zbl

[2] Brouwer, A. E., Haemers, W. H.: Eigenvalues and perfect matchings. Linear Algebra Appl. 395 (2005), 155-162. | MR | Zbl

[3] Chvátal, V.: New directions in Hamiltonian graph theory in New Directions in the Theory of Graphs. F. Harary Academic Press, New York (1973), 65-95. | MR

[4] Chvátal, V.: Tough graphs and hamiltonian circuits. Discrete Math. 306 (2006), 910-917. | DOI | MR

[5] Enomoto, H., Jackson, B., Katerinis, P.: Toughness and the existence of $k$-factors. Journal of Graph Theory 9 (1985), 87-95. | DOI | MR | Zbl

[6] Haemers, W. H.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 226-228 (1995), 593-616. | MR | Zbl

[7] Jung, H. A.: Note on Hamiltonian graphs, in Recent Advances in Graph Theory. M. Fiedler Academia, Prague (1975), 315-321. | MR

[8] Mohar, B.: A domain monotonicity theorem for graphs and hamiltonicity. Discrete Appl. Math. 36 (1992), 169-177. | DOI | MR | Zbl

[9] Heuvel, J. Vanden: Hamilton cycles and eigenvalues of graphs. Linear Algebra Appl. 226-228 (1995), 723-730. | MR