Naslov (eng)

Lower Bounds of the Kirchhoff and Degree Kirchhoff Indices

Autor

Glogić, Edin
Milovanović, Emina
Milovanović, Igor

Opis (eng)

Abstract: Let G be an undirected connected graph with n, n≥3, vertices and m edges. If μ_1≥μ_2≥⋯≥μ_n=0 and ρ_1≥ρ_2≥⋯≥ρ_(n-1)>ρ_n=0 are the Laplacian and the normalized Laplacian eigenvalues of G, then the Kirchhoff and degree Kirchhoff indices obey the relations Kf(G)=n∑_(i=1)^(n-1)▒1/μ_i and DKf(G)=2m∑_(i=1)^(n-1)▒1/ρ_i , respectively. The inequalities that determine lower bounds for some invariants of G, that contain Kf(G) and DKf(G), are obtained in this paper. Lower bounds for Kf(G) and DKf(G), known in the literature, are obtained as a special case.

Jezik

engleski

Datum

2015

Licenca

© All rights reserved

Predmet

Keywords: Kirchhoff index, Degree Kirchhoff index, Laplacian spectrum(of graph), normalized Laplacian spectrum(of graph).

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