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- W4381059992 abstract "Let G=(V,E) be a simple connected graph with vertex set V={1,2,…,n} and edge set E. The normalized Laplacian matrix of G is L=D−1/2(D−A)D−1/2, where D is the degree-diagonal matrix of G and A is the adjacency matrix of G. Let λ1≥λ2≥⋯≥λn−1≥λn=0 be the eigenvalues of L, for any real number α, the topological index sα∗(G) of G is defined as sα∗(G)=∑i=1n−1λiα.Let Ωij denote the resistance distance between vertices i and j, the degree-Kirchhoff index Kf∗(G) of G is defined as Kf∗(G)=∑i<jdidjΩij,where di is the degree of the vertex i. In this paper, we first express sα∗(G) in terms of Ωij’s explicitly for any real number α. Then as an application, we give a new proof for the classical Foster’s kth formula of resistance distances. Finally, we generalize the well-known relation 2|E|s−1∗(G)=Kf∗(G)to any integer k≥−1, which provides some upper bounds for sk∗(G)." @default.
- W4381059992 created "2023-06-18" @default.
- W4381059992 creator A5032895958 @default.
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- W4381059992 date "2023-10-01" @default.
- W4381059992 modified "2023-09-26" @default.
- W4381059992 title "On sum of powers of normalized Laplacian eigenvalues and resistance distances of graphs" @default.
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- W4381059992 doi "https://doi.org/10.1016/j.dam.2023.06.005" @default.
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