On Kirchhoff and degree Kirchhoff indices

Abstract

© 2015, University of Nis. All rights reserved. Let Gbe an undirected connected graph with n vertices and medges. If µ<inf>1</inf>≥ µ<inf>2</inf>≥ • • • ≥ µ<inf>n-1</inf>≥ µ<inf>n</inf>= 0 and ρ<inf>1</inf> ≥ ρ<inf>2</inf> ≥ • • • ≥ ρ<inf>n-1</inf>≥ ρ<inf>n</inf>= 0 are the Laplacian and the normalized Laplacian eigenvalues of G, then the Kirchhoff and the degree Kirchhoff indices obey the relations Kf(G) = (Formul Present)and DKf (G) =(Formul Present), respectively. Upper bounds for Kf(G) and DKf(G) are obtained.