A (signed) graph is said to exhibit the strong reciprocal (anti-reciprocal) eigenvalue property (SR) (resp., (-SR)) if for any eigenvalue λ, it has λ1 (resp.,- λ1 ) as an eigenvalue as well, with the same multiplicity. It is well known that the corona of a (signed) graph does have the property -SR, and if the graph has symmetric spectrum, then it also has the property SR. Therefore, it is interesting to identify (signed) graphs which are not corona graphs with the properties SR or -SR. Recently, a few constructions for unsigned graphs with the property -SR have been offered. In this article, we extend such constructions to signed graphs.
Signed graphs with strong (anti-)reciprocal eigenvalue property / Belardo, F.; Huntington, C.. - In: SPECIAL MATRICES. - ISSN 2300-7451. - 12:1(2024), pp. 1-28. [10.1515/spma-2024-0017]
Signed graphs with strong (anti-)reciprocal eigenvalue property
Belardo F.;Huntington C.
2024
Abstract
A (signed) graph is said to exhibit the strong reciprocal (anti-reciprocal) eigenvalue property (SR) (resp., (-SR)) if for any eigenvalue λ, it has λ1 (resp.,- λ1 ) as an eigenvalue as well, with the same multiplicity. It is well known that the corona of a (signed) graph does have the property -SR, and if the graph has symmetric spectrum, then it also has the property SR. Therefore, it is interesting to identify (signed) graphs which are not corona graphs with the properties SR or -SR. Recently, a few constructions for unsigned graphs with the property -SR have been offered. In this article, we extend such constructions to signed graphs.| File | Dimensione | Formato | |
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