The Complete Classification of Graphs whose Second Largest Eigenvalue of the Eccentricity Matrix is Less Than 1  

作　　者：Jian Feng WANG Xing Yu LEI Shu Chao LI Zoran STANIC 

机构地区：[1]School of Mathematics and Statistics,Shandong University of Technology,Zibo,255049,P.R.China [2]Faculty of Mathematics and Statistics,Central China Normal University,Wuhan,430079,P.R.China [3]Faculty of Mathematics,University of Belgrade,Studentski trg 16,11000,Belgrade,Serbia

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1741-1766,共26页数学学报（英文版）

基　　金：supported by the Special Fund for Taishan Scholars Project;the IC Program of Shandong Institutions of Higher Learning For Youth Innovative Talents;supported by the National Natural Science Foundation of China (Grant No. 12371353);supported by the Science Fund of the Republic of Serbia grant number 7749676:Spectrally Constrained Signed Graphs with Applications in Coding Theory and Control Theory–SCSG-ctct

摘　　要：The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column,and replacing the remaining entries by zero.This matrix can be interpreted as an opposite to the adjacency matrix,which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1.In the paper,we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1.

关 键 词：Eccentricity matrix EIGENVALUE diameter principal submatrix forbidden subgraph 

分 类 号：O151.21[理学—数学] O157.5[理学—基础数学]