کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4598787 | 1631103 | 2016 | 8 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). Let D(G)D(G) be the distance matrix of G. For a given nonnegative integer k, when n is sufficiently large with respect to k , we show that λn−k(D)≤−1λn−k(D)≤−1, thereby solving a problem proposed by Lin et al. (2014) [8]. The distance Laplacian spectral radius of a connected graph G is the spectral radius of the distance Laplacian matrix of G, defined asDL(G)=Tr(G)−D(G),DL(G)=Tr(G)−D(G), where Tr(G)Tr(G) is the diagonal matrix of vertex transmissions of G. Aouchiche and Hansen (2014) [3] conjectured that m(λ1(DL))≤n−2m(λ1(DL))≤n−2 when G≇KnG≇Kn, and the equality holds if and only if either G≅K1,n−1G≅K1,n−1 or G≅Kn2,n2. In this paper, we confirm the conjecture.
Journal: Linear Algebra and its Applications - Volume 492, 1 March 2016, Pages 128–135