Comptes Rendus
no. 6
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

Vladimir Nikiforov1
1 Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA
Comptes Rendus. Mathématique, Volume 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.03.013

Vladimir Nikiforov 1

1 Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA 
@article{CRMATH_2015__353_6_471_0,
     author = {Vladimir Nikiforov},
     title = {The trace norm of \protect\emph{r}-partite graphs and matrices},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {471--475},
     publisher = {Elsevier},
     volume = {353},
     number = {6},
     year = {2015},
     doi = {10.1016/j.crma.2015.03.013},
     language = {en},
}
TY  - JOUR
AU  - Vladimir Nikiforov
TI  - The trace norm of r-partite graphs and matrices
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 471
EP  - 475
VL  - 353
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2015.03.013
LA  - en
ID  - CRMATH_2015__353_6_471_0
ER  - 
%0 Journal Article
%A Vladimir Nikiforov
%T The trace norm of r-partite graphs and matrices
%J Comptes Rendus. Mathématique
%D 2015
%P 471-475
%V 353
%N 6
%I Elsevier
%R 10.1016/j.crma.2015.03.013
%G en
%F CRMATH_2015__353_6_471_0
Vladimir Nikiforov. The trace norm of r-partite graphs and matrices. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 471-475. doi : 10.1016/j.crma.2015.03.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.013/

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

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

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

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

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

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

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

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

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

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

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

Cité par Sources :

Commentaires - Politique