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- W3208141921 abstract "We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to Hermitian matrices, with focus on the generalized adjacency matrix and the generalized normalized adjacency matrix. We then determine necessary and sufficient conditions such that a pair of twin vertices in a weighted graph exhibits strong cospectrality with respect to the above-mentioned matrices. We also determine when strong cospectrality is preserved under Cartesian and direct products of graphs. Moreover, we generalize known results about equitable and almost equitable partitions and use these to determine which joins of the form $Xvee H$, where $X$ is either the complete or empty graph, exhibit strong cospectrality." @default.
- W3208141921 created "2021-11-08" @default.
- W3208141921 creator A5011633377 @default.
- W3208141921 date "2022-09-10" @default.
- W3208141921 modified "2023-10-14" @default.
- W3208141921 title "Strong cospectrality and twin vertices in weighted graphs" @default.
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- W3208141921 doi "https://doi.org/10.13001/ela.2022.6721" @default.
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