On the eccentricity spectra of complete multipartite graphs

作者：Wei, Wei; Li, Shuchao^*

来源：APPLIED MATHEMATICS AND COMPUTATION, 2022, 424: 127036.

DOI：10.1016/j.amc.2022.127036

• Eccentricity matrix
• epsilon-spectrum
• Majorization
• Multiplicity

The eccentricity matrix epsilon(G) of a graph G is derived from the corresponding distance matrix by keeping only the largest non-zero elements for each row and each column and leaving zeros for the remaining ones. The epsilon-eigenvalues of a graph G are those of its eccentricity matrix, in which the maximum modulus is called the epsilon-spectral radius. In this paper, we first establish the relationship between the majorization and epsilon-spectral radii of complete multipartite graphs. As applications, the extremal complete multipartite graphs having the minimum and maximum epsilon-spectral radii are determined. Furthermore, we study the multiplicities of epsilon-eigenvalues among complete multipartite graphs and identify all complete multipartite graphs with distinct epsilon-eigenvalues.