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- W2017973357 abstract "Let G=(V,E) be a simple, connected and undirected graph with vertex set V(G) and edge set E(G). Also let D(G) be the distance matrix of a graph G (Janežič et al., 2007) [13]. Here we obtain Nordhaus–Gaddum-type result for the spectral radius of distance matrix of a graph. A sharp upper bound on the maximal entry in the principal eigenvector of an adjacency matrix and signless Laplacian matrix of a simple, connected and undirected graph are investigated in Das (2009) [4] and Papendieck and Recht (2000) [15]. Generally, an upper bound on the maximal entry in the principal eigenvector of a symmetric nonnegative matrix with zero diagonal entries and without zero diagonal entries are investigated in Zhao and Hong (2002) [21] and Das (2009) [4], respectively. In this paper, we obtain an upper bound on minimal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs. Moreover, we present the lower and upper bounds on maximal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs." @default.
- W2017973357 created "2016-06-24" @default.
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- W2017973357 date "2011-11-01" @default.
- W2017973357 modified "2023-09-24" @default.
- W2017973357 title "Maximal and minimal entry in the principal eigenvector for the distance matrix of a graph" @default.
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- W2017973357 doi "https://doi.org/10.1016/j.disc.2011.07.034" @default.
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