文献类型：期刊文献

英文题名：Spectral extrema of graphs: Forbidden hexagon

作者：Zhai, Mingqing[1];Lin, Huiqiu[2]

机构：[1]Chuzhou Univ, Sch Math & Finance, Chuzhou 239012, Anhui, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2020

卷号：343

期号：10

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000558591300031)】；

基金：Supported by National Natural Science Foundation of China (Nos. 11971445, 11771141 and 12011530064), the key talents project of Anhui Province, China (No. GXBJZD2016082).

语种：英文

外文关键词：Path; Cycle; Spectral radius; Adjacency matrix; Hexagon

摘要：To determine the Turan numbers of even cycles is a central problem of extremal graph theory. Even for C-6, the Turan number is still open. Till now, the best known upper bound is given by Faredi, Naor and Verstraete [On the Turan number for the hexagon, Advances in Math.]. In 2010, Nikiforov posed a spectral version of extremal graph theory problem: what is the maximum spectral radius rho of an H-free graph of order n? Let ex(sp)(n, H) = max{rho(G)vertical bar vertical bar V(G)vertical bar= n, H not subset of G}. In contrast to the unsolved problem of Turan number of C-6, we obtain the exact value of ex(sp)(n, C-6) and characterize the unique extremal graph. The result also confirms Nikiforov's conjecture [The spectral radius of graphs without paths and cycles of specified length, Linear Algebra Appl.] for k = 2. (C) 2020 Elsevier B.V. All rights reserved.