Graphs with few distinct eigenvalues and extremal energy

Autores

  • Nelcy E. Arévalo IME/UFRGS
  • Rodrigo O. Braga IME/UFRGS
  • Virgínia M. Rodrigues IME/UFRGS

Resumo

Among the various spectral parameters studied in the Spectral Graph Theory, one can highlighttheenergyof a graph, introduced by I. Gutman in 1978 [4]. The energy of a graphGwithnverticesis defined as [...]

Downloads

Não há dados estatísticos.

Referências

Ar ́evalo, N.E, Braga, R.O. and Rodrigues V.M. Graphs with few distinct eigenval-ues and extremal energy,Linear Algebra and its Applications, 620:147-167, 2021. DOI:10.1016/j.laa.2021.02.027.

Bridges, W.G. and Mena, R.A. Multiplicative cones – a family of three eigenvalue graphs,Aequationes Mathematicae, 22:208–214, 1981. DOI: 10.1007/BF02190180.

Chuang, H. and Omidi, G. Graphs with three distinct eigenvalues and largest eigen-value less than 8,Linear Algebra and its Applications, 430:2053–2062, 2009. DOI:10.1016/j.laa.2008.11.028.

Gutman, I. The energy of a graph,Ber. Math.– Statist. Sekt. Forschungsz. Graz, 103:1–22,1978.

Huang, X. and Huang, Q. On regular graphs with four distinct eigenvalues,Linear Algebraand its Applications, 512:219–233, 2017. DOI: 10.1016/j.laa.2016.09.043.

Koolen, J. and Moulton, V. Maximal energy graphs,Advances in Applied Mathematics, 26:47–52, 2001. DOI: 10.1006/aama.2000.0705

.[7] Li, X., Shi, Y. and Gutman, I.Graph Energy. Springer, New York, 2012.

Muzychuk, M. and Klin, M. On graphs with three eigenvalues,Discrete Mathematics, 189:191–207, 1998. DOI: 10.1016/S0012-365X(98)00084-3.

Nikiforov, V. The energy of graphs and matrices,Journal of Mathematical Analysis and Ap-plications, 326:1472–1475, 2007. DOI: 10.1016/j.jmaa.2006.03.072.

Nikiforov, V. Beyond graph energy: Norms of graphs and matrices,Linear Algebra and itsApplications, 506:82–138, 2015. DOI: 10.1016/j.laa.2016.05.011.

Van Dam, E.R. Regular graphs with four eigenvalues,Linear Algebra and its Applications,226-228:139–162, 1995. DOI: 10.1016/0024-3795(94)00346-F.

Van Dam, E.R. Graphs with few eigenvalues. An interplay between combinatorics and algebra,Doctoral Thesis, Tilburg University, 1996.

Van Dam, E.R. Nonregular graphs with three eigenvalues,Journal of Combinatorial Theory,Series B,, 73:101–118, 1998. DOI: 10.1006/jctb.1998.1815.

Downloads

Publicado

2021-12-20

Edição

Seção

Resumos