On a version of the spectral excess theorem
| Main Authors: | Fiol, Miquel Àngel; Departament de Matem\`atiques, Universitat Polit\' ecnica de Catalunya, Barcelona Graduate School of Mathematics, Catalonia, Spain, Penjic, Safet; Andrej Maru\v{s}i\v{c} Institute, University of Primorska, Muzejski trg 2 6000 Koper, Slovenia |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2020
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/904 https://www.ejgta.org/index.php/ejgta/article/view/904/pdf_147 |
Daftar Isi:
- Given a regular (connected) graph G=(X,E) with adjacency matrix A, d+1 distinct eigenvalues, and diameter D, we give a characterization of when its distance matrix AD is a polynomial in A, in terms of the adjacency spectrum of G and the arithmetic (or harmonic) mean of the numbers of vertices at distance at most D-1 from every vertex. The same result is proved for any graph by using its Laplacian matrix L and corresponding spectrum. When D=d we reobtain the spectral excess theorem characterizing distance-regular graphs.