o:29177 Lower Bounds of the Kirchhoff and Degree Kirchhoff Indices en 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. Keywords: Kirchhoff index, Degree Kirchhoff index, Laplacian spectrum(of graph), normalized Laplacian spectrum(of graph). 1552101 2217-5539 2023-05-08T13:26:25.208Z 44 no 46 Igor Milovanović 0000-0003-2209-9606 Emina Milovanović person 0000-0002-1905-4813 Edin Glogić Državni univerzitet u Novom Pazaru person 0000-0001-6295-8298 application/pdf 54615 https://phaidrabg.bg.ac.rs/o:29177 no yes 1 70 92000001 20A01 Scientific Publications of the State University of Novi Pazar, Ser. A: Appl. Math. Inform. and Mech. 7 1 25 31 2015