Laplacian energy of trees with at most 10 vertices
Abstract
Let Tn be the set of all trees with n ≤ 10 vertices. We show that the Laplacian energy of any tree Tn is strictly between the Laplacian energy of the path Pn and the star Sn, the authors partially proving that the conjecture hold for any tree Tn, where n ≤ 10.
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PDFDOI: http://dx.doi.org/10.19184/ijc.2018.2.1.3
References
D. M. Cvetkovic ́, M. Doob and H. Sachs, Spectra of Graphs− Theory and Application, Vol. 87. Academic Press, 1980.
I. Gutman, The energy of a graph, Ber. Math.Statist. Sekt. Forschungsz. Graz, 103 (1978), 1–22.
I. Gtman, Total π-electron energy of benzenoid hydrocarbons,, Topics Curr. Chem., 162 (1992), 29–63.
I. Gutman, The energy of a graph: old and new results,in: A. Betten, A. Kohnert, R. Laue, A. Wassermann(Eds.), Algebraic Combinatorics and Applications, Springer-Verlag, Berlin (2001) 196–211.
I. Gutman, B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414 (2006), 29–37.
D.M. Cardoso, D. Cvetkovic ́, P. Rowlinson, S. Simic ́, A sharp lower bound for the least eigen-value of the signless Laplacian of a non-bipartite graph, Linear Algebra Appl. 429 (2008), 2770-2780.
I. Gutman, Acyclic systems with extremal Hu ̈ckel π-electron energy, Theor. Chim. Acta 45 (1977), 79–87.
S. Radenkovic ́, I. Gutman, Total π-electron energy and Laplacian energy: how far the analogy goes? J. Serb. Chem. Soc. 72(12) (2007) 1343–1350.
V. Trevisan, J. B. Carvalho, Renata R. Del Vecchio, Cybele T.M. Vinagre, Laplacians energy of diameter 3 trees, Appl. Math. Lett., 24 (2011) 918–923.
R. C. Read, R. J. Wilson, An Atlas of Graphs, The Clarendon Press Oxford University Press, NewYork, 1998.
D. Stevanovic ́, I. Gutman, M. U. Rehman, On spectral radius and energy of complete multi- partite graphs, Ars Mathematica Contemporanea 9 (2015), 109-113.
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