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2020, vol. 68, br. 1, str. 1-7
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Nova ograničenja za Laplasovu energiju
New bounds for Laplacian energy
Univerzitet u Kragujevcu, Prirodno-matematički fakultet
e-adresa: gutman@kg.ac.rs
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.
Abstract
Introduction/purpose: The Laplacian energy (LE) is the sum of absolute values of the terms μi-2m/n, where μi, i=1,2,…,n, are the eigenvalues of the Laplacian matrix of the graph G with n vertices and m edges. The basic results of the theory of LE are outlined, and some new obtained. Methods: Spectral theory of Laplacian matrices is applied. Results: A new class of lower bounds for LE is derived. Conclusion: The paper contributes to the Laplacian spectral theory and tp the theory of graph energies.
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