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Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
Huicai Jia1,2, Hongye Song2,3
1College of Science, Henan Institute of Engineering, Zhengzhou, P.R. China.
Abstract:
Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let [Formula: see text], [Formula: see text] and [Formula: see text] be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, respectively. In this paper, we give lower bounds on [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and the corresponding extremal graphs are also characterized.
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