On the eccentricity matrix of graphs and its applications to the boiling point of hydrocarbons

• Published in: Chemometrics and intelligent laboratory systems Vol. 207; p. 104173
• Main Authors: Wang, Jianfeng, Lei, Xingyu, Wei, Wei, Luo, Xiaobing, Li, Shuchao
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.12.2020
• Subjects: Boiling point AMS subject classification: 05C50; Eccentricity matrix; Least eigenvalue; Spectral determination; Spectral radius; Least eigenvalue; Spectral determination; Boiling point AMS subject classification: 05C50; Spectral radius; Eccentricity matrix
• ISSN: 0169-7439; 1873-3239
• DOI: 10.1016/j.chemolab.2020.104173

The eccentricity matrix E(G) of a graph G is derived from the distance matrix by keeping for each row and each column only the largest distances and leaving zeros in the remaining ones. The E-eigenvalues of a graph G are those of its eccentricity matrix E(G). The E-spectrum of the graph G is the multiset of its E-eigenvalues, where the maximum modulus is called the E-spectral radius of G. In this paper, we characterize the graphs whose E-spectral radius attains the minimum (resp. the second minimum) value and the graphs maximizing the least and the second least E-eigenvalues. As a by-product, the graphs with ξ(G)=diam(G) or ζ(G)=−diam(G) for diam(G)∈{1,2} are identified, where diam(G) denotes the diameter of G. Furthermore, we determine the graphs other than K1,n1,…,n6(ni≥2,i∈1,…,6) whose least E-eigenvalue is equal to −22. Additionally, the E-spectral determination of graphs is investigated. At last some numerical results are discussed, in which the linear models for the E-spectral radius (resp. E-energy) are better than or as good as the models corresponding to the spectral radius (resp. energy) in terms of some parameters. •Spectral properties of the eccentricity matrix are studied.•A regression analysis of the linear models of benzenoid hydrocarbons with the spectral radius and some distance-based indices have been carried out.