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- W2041093075 abstract "Let G=(V,E) be a digraph with n vertices and m arcs without loops and multiarcs, V={v1,v2,…,vn}. Denote by ρ(G) the largest eigenvalue of its adjacency matrix, Wk(i) the number of k-walks from vertex vi. In this paper, we prove that the inequalities minWp+q(i)Wq(i):vi∈V⩽ρp(G)⩽maxWp+q(i)Wq(i):vi∈V hold for every integers p⩾1,q⩾0. If G is strongly connected, then each equality holds iff Wp+q(1)Wq(1)=Wp+q(2)Wq(2)=⋯=Wp+q(n)Wq(n) . Furthermore, we have limp→∞Wp+q(i)Wq(i)1p=ρ(G) for every integers p⩾1,q⩾0 and each vertex vi∈V(G)." @default.
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- W2041093075 date "2012-12-01" @default.
- W2041093075 modified "2023-09-23" @default.
- W2041093075 title "Bounds on the spectral radii of digraphs in terms of walks" @default.
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- W2041093075 doi "https://doi.org/10.1016/j.amc.2012.09.073" @default.
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