On the eccentricity spectra of complete multipartite graphs

Wei Wei and Shuchao Li

Applied Mathematics and Computation, 2022, vol. 424, issue C

Abstract: The eccentricity matrix E(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 E-eigenvalues of a graph G are those of its eccentricity matrix, in which the maximum modulus is called the E-spectral radius. In this paper, we first establish the relationship between the majorization and E-spectral radii of complete multipartite graphs. As applications, the extremal complete multipartite graphs having the minimum and maximum E-spectral radii are determined. Furthermore, we study the multiplicities of E-eigenvalues among complete multipartite graphs and identify all complete multipartite graphs with distinct E-eigenvalues.

Keywords: Eccentricity matrix; E-spectrum; Majorization; Multiplicity (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322001229

DOI: 10.1016/j.amc.2022.127036

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