A ug 2 00 6 Bounds on graph eigenvalues
نویسنده
چکیده
We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of order n ≥ 2, maximum degree ∆, and girth at least 5, then μ (G) ≤ min {
منابع مشابه
1 2 M ay 2 00 6 Bounds on graph eigenvalues
We refute, improve or amplify some recent results on graph eigenvalues. In particular, we prove that if G is a graph of order n ≥ 2, maximum degree ∆, and girth at least 5, then the maximum eigenvalue μ (G) of the adjacency matrix of G satisfies μ (G) ≤ min {
متن کاملOn the eigenvalues of some matrices based on vertex degree
The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.
متن کاملSome remarks on the sum of the inverse values of the normalized signless Laplacian eigenvalues of graphs
Let G=(V,E), $V={v_1,v_2,ldots,v_n}$, be a simple connected graph with $%n$ vertices, $m$ edges and a sequence of vertex degrees $d_1geqd_2geqcdotsgeq d_n>0$, $d_i=d(v_i)$. Let ${A}=(a_{ij})_{ntimes n}$ and ${%D}=mathrm{diag }(d_1,d_2,ldots , d_n)$ be the adjacency and the diagonaldegree matrix of $G$, respectively. Denote by ${mathcal{L}^+}(G)={D}^{-1/2}(D+A) {D}^{-1/2}$ the normalized signles...
متن کامل2 4 A ug 2 00 6 New lower bounds for the number of ( ≤ k ) - edges and the rectilinear crossing number of K n ∗
We provide a new lower bound on the number of (≤ k)-edges of a set of n points in the plane in general position. We show that for 0 ≤ k ≤ ⌊ 2 ⌋ the number of (≤ k)-edges is at least Ek(S) ≥ 3 (
متن کاملA note on the bounds of Laplacian-energy-like-invariant
The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the num...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008