کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599884 | 1336826 | 2013 | 15 صفحه PDF | دانلود رایگان |
Let G=(V,E)G=(V,E) be a simple graph with vertex set V(G)={v1,v2,…,vn}V(G)={v1,v2,…,vn} and edge set E(G)E(G). The Laplacian matrix of G is L(G)=D(G)−A(G)L(G)=D(G)−A(G), where D(G)D(G) is the diagonal matrix of its vertex degrees and A(G)A(G) is the adjacency matrix. Let μ1⩾μ2⩾⋯⩾μn−1⩾μn=0μ1⩾μ2⩾⋯⩾μn−1⩾μn=0 be the Laplacian eigenvalues of G. For a graph G and a real number β≠0β≠0, the graph invariant Sβ(G)Sβ(G) is the sum of the β-th power of the non-zero Laplacian eigenvalues of G, that is,Sβ(G)=∑i=1n−1μiβ.In this paper, we obtain some lower and upper bounds on Sβ(G)Sβ(G) for G in terms of n, the number of edges m , maximum degree Δ1Δ1, clique number ω, independence number α and the number of spanning trees t . Moreover, we present some Nordhaus–Gaddum-type results for Sβ(G)Sβ(G) of G.
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3561–3575