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Orthogonal symmetric matrices and joins of graphs.
- Source :
-
Linear Algebra & its Applications . Nov2022, Vol. 652, p213-238. 26p. - Publication Year :
- 2022
-
Abstract
- We introduce a notion of compatibility for multiplicity matrices. This gives rise to a necessary condition for the join of two (possibly disconnected) graphs G and H to be the pattern of an orthogonal symmetric matrix, or equivalently, for the minimum number of distinct eigenvalues q of G ∨ H to be equal to two. Under additional hypotheses, we show that this necessary condition is also sufficient. As an application, we prove that q (G ∨ H) is either two or three when G and H are unions of complete graphs, and we characterise when each case occurs. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 652
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 158608419
- Full Text :
- https://doi.org/10.1016/j.laa.2022.07.007