Combinatorics
The trace norm of r-partite graphs and matrices
[La norme de trace des graphes et des matrices r-partis]

Présenté par : Michèle Vergne

Nikiforov, Vladimir1
1 Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA
Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 471-475.

La norme de trace de graphes a été beaucoup étudiée sous le nom d'énergie de graphe. Cette note présente des bornes à la norme de trace maximale d'un graphe r-parti d'ordre n. Les bornes inférieures proviennent des matrices de conférence et de Hadamard.

The trace norm of graphs has been widely studied under the name graph energy. This note presents bounds on the maximum trace norm of an r-partite graph of order n. The lower bounds come from conference and Hadamard matrices.

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Accepté le :
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DOI : 10.1016/j.crma.2015.03.013
Nikiforov, Vladimir 1

1 Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA 
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Nikiforov, Vladimir. The trace norm of r-partite graphs and matrices. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 471-475. doi : 10.1016/j.crma.2015.03.013. http://www.numdam.org/articles/10.1016/j.crma.2015.03.013/

[1] Craigen, R.; Kharaghani, H. Hadamard matrices and Hadamard designs (Colbourn, C.; Dinitz, J.H., eds.), Handbook of Combinatorial Designs, Chapman & Hall/CRC Press, Boca Raton, FL, USA, 2006, pp. 273-280

[2] Cvetković, D. Chromatic number and the spectrum of a graph, Publ. Inst. Math. (Belgr.), Volume 14 (1972) no. 28, pp. 25-38

[3] Delorme, C. Eigenvalues of complete multipartite graphs, Discrete Math., Volume 312 (2012), pp. 2532-2535

[4] Gutman, I. The energy of a graph, Ber. Math.-Stat. Sekt. Forschungszent. Graz, Volume 103 (1978), pp. 1-22

[5] Gutman, I.; Li, X.; Shi, Y. Graph Energy, Springer, New York, 2012 (266 pp)

[6] Haemers, W. Strongly regular graphs with maximal energy, Linear Algebra Appl., Volume 429 (2008), pp. 2719-2723

[7] Hoffman, A.J. On eigenvalues and colorings of graphs, Graph Theory and Its Applications, Academic Press, New York, 1970, pp. 79-91

[8] Ionin, Y.; Kharaghani, H. Balanced generalized weighing matrices and conference matrices (Colbourn, C.; Dinitz, J.H., eds.), Handbook of Combinatorial Designs, Chapman & Hall/CRC Press, Boca Raton, FL, USA, 2006, pp. 273-280

[9] Koolen, J.H.; Moulton, V. Maximal energy graphs, Adv. Appl. Math., Volume 26 (2001), pp. 47-52

[10] Koolen, J.H.; Moulton, V. Maximal energy bipartite graphs, Graphs Comb., Volume 19 (2003), pp. 131-135

[11] Stevanović, D.; Gutman, I.; Rehman, M.U. On spectral radius and energy of complete multipartite graphs, Ars Math. Contemp., Volume 9 (2015), pp. 109-113

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