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Solutions for two conjectures on the eigenvalues of the eccentricity matrix, and beyond

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成果类型:
期刊论文
作者:
Wei, Wei;He, Xiaocong;Li, Shuchao*
通讯作者:
Li, Shuchao
作者机构:
[He, Xiaocong; Wei, Wei; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Li, Shuchao] C
Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
语种:
英文
关键词:
Diameter;Spectral radius;The eccentricity matrix;The least eigenvalue
期刊:
Discrete Mathematics
ISSN:
0012-365X
年:
2020
卷:
343
期:
8
页码:
111925
基金类别:
S.L. acknowledges the financial support from the National Natural Science Foundation of China (Grant Nos. 11671164 , 11771172 ) and the excellent doctoral dissertation cultivation grant from Central China Normal University (Grant No. 2019YBZZ061 ).
机构署名:
本校为第一且通讯机构
院系归属:
数学与统计学学院
摘要:
The eccentricity matrix epsilon(G) of a graph G is constructed from the distance matrix of G by keeping only the largest distances for each row and each column. This matrix can be interpreted as the opposite of the adjacency matrix obtained from the distance matrix by keeping only the distances equal to 1 for each row and each column. In this paper we focus on the eccentricity matrix of graphs. Let T be an n-vertex tree and let epsilon(n)(T) be the least epsilon-eigenvalue of T. On the one hand, we determine the n-vertex trees with the minimum epsilon-spectral radius. On the other hand, for n ...

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