# FURTHER RESULTS REGARDING THE DEGREE KIRCHHOFF INDEX OF GRAPHS

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Let G be a simple graph of order N. The normalized Laplacian Estrada index of G is defined as NEE(G) = âˆ‘Ni=1eÎ»i-1, where Î»1, Î»2 â‹¯, Î»N the normalized Laplacian eigenvalues of G. In this paper, we give a tight lower bound for NEE of general graphs. We also calculate NEE for...

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Let G be a binary labeled graph and Al (G) = (lij) be its label adjacency matrix. For a vertex vi, we define label degree as ... . In this paper, we define label Laplacian energy LEl (G). It depends on the underlying graph G and labels of the vertices. We compute label Laplacian spectrum of...

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Let L be the Laplace matrix of a weighted digraph. The aim of the paper is to establish a simple way for computing any coefficient of the characteristic polynomial of L as a constant sign sum over the incoming spanning forests. The idea is to express L as the product of generalized (weighted)...