The largest eigenvalue of nonregular graphs
نویسنده
چکیده
We give an upper bound for the largest eigenvalue of a nonregular graph with n vertices and the largest vertex degree ∆.
منابع مشابه
Extreme eigenvalues of nonregular graphs
Let λ1 be the greatest eigenvalue and λn the least eigenvalue of the adjacency matrix of a connected graph G with n vertices, m edges and diameter D. We prove that if G is nonregular, then Δ− λ1 > nΔ− 2m n(D(nΔ− 2m)+ 1) 1 n(D + 1) , where Δ is the maximum degree of G. The inequality improves previous bounds of Stevanović and of Zhang. It also implies that a lower bound on λn obtained by Alon an...
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 91 شماره
صفحات -
تاریخ انتشار 2004