Nova ograničenja za Laplasovu energiju

  • Ivan Gutman Univerzitet u Kragujevcu, Prirodno-matematicki fakultet
Ključne reči: spectral graph theory||, ||spektralna teorija grafova, Laplacian spectrum (of graph)||, ||Laplasov spektar (grafa), Laplacian energy||, ||Laplasova energija,

Sažetak


Uvod/svrha: Laplasova energija (LE) grafa je suma apsolutnih vrednosti izraza μi-2m/n, gde μi, i=1,2,…,n, predstavljaju sopstvene vrednosti Laplasove matrice grafa G sa n čvorova i m grana. Pored osnovnih rezultata teorije Laplasove energije dati su i neki novodobijeni.

Metode: Korišćena je spektralna teorija Laplasovih matrica.

Rezultati: Izvodi se nova klasa donjih ograničenja za Laplasovu energiju.

Zaključak: Rad daje doprinos Laplasovoj spektralnoj teoriji kao i teoriji energija grafa.

 

Biografija autora

Ivan Gutman, Univerzitet u Kragujevcu, Prirodno-matematicki fakultet
www.pmf.kg.ac.rs/gutman

Reference

Andriantiana, E.O.D. 2016. Laplacian energy. In: Gutman, I. & Li, X. (Eds.), Graph Energies - Theory and Applications.Kragujevac: University of Kragujevac, pp.49-80.

Borovićanin, B., Das, K.C., Furtula, B., & Gutman, I. 2017. Bounds for Zagreb indices. MATCH Communications in Mathematical and in Computer Chemistry, 78(1), pp.17-100 [online]. Available at: http://match.pmf.kg.ac.rs/electronic_versions/Match78/n1/match78n1_17-100.pdf. [Accessed: 30 November 2019]

Cvetković, D. 1981. Teorija grafova i njene primene.Belgrade: Naučna knjiga (in Serbian).

Grone, R., Merris, R., & Sunder, V.S. 1990. The Laplacian Spectrum of a Graph. SIAM Journal on Matrix Analysis and Applications, 11(2), pp.218-238. Available at: https://doi.org/10.1137/0611016.

Gutman, I. 2019. Oboudi-type bounds for graph energy. Mathematics Interdisciplinary Research, 4(2), pp.151-155 [online]. Available at: http://mir.kashanu.ac.ir/article_96938_35e2a0e7a15dcdd1e796325b33542469.pdf. [Accessed: 30 November 2019]

Gutman, I., & Furtula, B. 2019. Graph Energies: Survey, Census, Bibliography.Kragujevac: Centar SANU. Bibliography.

Gutman, I., & Zhou, B. 2006. Laplacian energy of a graph. Linear Algebra and its Applications, 414(1), pp.29-37. Available at: https://doi.org/10.1016/j.laa.2005.09.008.

Harary, F. 1969. Graph Theory.Addison-Wesley. Reading.

Li, X., Shi, Y., & Gutman, I. 2012. Introduction. In: Graph Energy.New York, NY: Springer Science and Business Media LLC., pp.1-9. Available at: https://doi.org/10.1007/978-1-4614-4220-2_1.

Merris, R. 1994. Laplacian matrices of graphs: A survey. Linear Algebra and its Applications, 197-198, pp.143-176. Available at: https://doi.org/10.1016/0024-3795(94)90486-3.

Oboudi, M.R. 2019. A new lower bound for the energy of graphs. Linear Algebra and its Applications, 580, pp.384-395. Available at: https://doi.org/10.1016/j.laa.2019.06.026.

Objavljeno
2019/12/06
Rubrika
Originalni naučni radovi