Jia Huicai, Song Hongye
College of Science, Henan Institute of Engineering, Zhengzhou, P.R. China.
2Department of Mathematics, School of Information, Renmin University of China, Beijing, P.R. China.
J Inequal Appl. 2018;2018(1):69. doi: 10.1186/s13660-018-1663-5. Epub 2018 Apr 3.
Let be a connected graph of order . The remoteness of , denoted by , is the maximum average distance from a vertex to all other vertices. Let [Formula: see text], [Formula: see text] and [Formula: see text] be the distance, distance Laplacian and distance signless Laplacian eigenvalues of , respectively. In this paper, we give lower bounds on [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and the corresponding extremal graphs are also characterized.
设(G)是一个阶数为(n)的连通图。(G)的离心率，记为(r(G))，是一个顶点到所有其他顶点的最大平均距离。设(d(G))、(D(G))和(Q(G))分别是(G)的距离、距离拉普拉斯和距离无符号拉普拉斯特征值。在本文中，我们给出了(r(G))、(d(G))、(D(G))、(Q(G))的下界，并刻画了相应的极值图。
