On applications of Andrica-Badea and Nagy inequalities in spectral graph theory
Keywords:
Inequalities, first Zagreb index, spread of graph.Abstract
Applications of Andrica-Badea and Nagy inequalities for determining bounds of graph invariants of undirected, connected graphs are investigated. We consider bounds of the following invariants: the first Zagreb index, general Randic index, Laplacian linear spread and normalized Laplacian spread of graphs.
Mathematics Subject Classification (2010): 60E15, 05C50.
References
Andrica, D., Badea, C., Grus inequality for positive linear functionals, Period. Math. Hungar, 19(1988), no. 2, 155{167.
Bell, F.K., A note on the irregularity of graphs, Lin. Algebra Appl., 161(1992), 45-54.
Biggs, N., Algebraic graph theory, Cambridge Univ. Press, Cambridge, UK, 1993.
Butler, S., Eigenvalues and structures of graph, Ph. Dissertation, University of California, San Diego, 2008.
de Caen, D., An upper bound on the sum of squares of degrees in a graph, Discr. Math., 185(1998), no. 1-3, 245{248.
Cavers, M., Fallat, S., Kirkland, S., On the normalized Laplacian energy and general Randic index of graphs, Lin. Algebra Appl., (2010), no. 433, 172-190.
Chung, F.R.K., Spectral graph theory, Am. Math. Soc., Providence, 1997.
Cvetkovi_c, D., Doob, M., Sachs, H., Spectra of graph theory and application, New York, Academic Press, 1980.
Edwards, C.S., The largest vertex degre sum for a triangle of a graph, Bull. London Math. Soc., 9(1977), 203{208.
Fath-Tabar, G.H., Ashra, A.R., Some remark on Laplacian eigenvalues of graphs, Math. Commun., 15(2010), no. 2, 443-451.
Goldberg, F., New results on eigenvalues on degree deviation http://orXivorg.1403.269V1, 2014.
Gutman, I., Furtula, B., Elphick, C., Tree new/old vertex-degree based toplogoical indices, MATCH Commun. Math. Comput. Chem., 72(2014), 617-632.
Gutman, I., Trinajstic, N., Graph theory and molecular orbitas. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Letters, 17(1972), 535-538.
Li, X., Yang, Y., Sharp bounds for the general Randic index, MATCH Commun. Math. Comput. Chem., 51(2004), 155-166.
Merris, R., Laplacian matrices of graphs: A survey, Lin. Algebra Appl., 197-198(1994), 143-176.
Milovanovic, I., Milovanovic, E., Remark on inequalities for the Laplacian spread of graphs, Czeh. Math. J., 64 (2014), no. 139, 285-287.
Nagy, J.V.S., Uber algebraische Gleichungen mit lauter reellen Wurzeln, Jahresbericht der deutschen mathematiker-Vereingung, 27(1918), 37-43.
Randic, M., On characterization of molecular branching, J. Amer. Chem. Soc., 97(1975), 6609-6615.
Zumstein, P., Comparison of spectral methods through the adjacency matrix and the Laplacian of a graph, Ph. Dissertation, ETH Zurich, 2005.
You, Z., Liu, B., The Laplacian spread of graphs, Czech. Math. J., 62(2012), 159-168.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
