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- W4360596391 abstract "In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$. The spectrum of $G$ is referring to its adjacency matrix, and the spectrum of $G^m$ is referring to its adjacency tensor. The graph $G$ is called determined by high-ordered spectra (DHS for short) if, whenever $H$ is a graph such that $H^m$ is cospectral with $G^m$ for all $m$, then $H$ is isomorphic to $G$. In this paper we first give formulas for the traces of the power of unicyclic graphs, and then provide some high-ordered cospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with different high-ordered spectra." @default.
- W4360596391 created "2023-03-24" @default.
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- W4360596391 date "2023-01-01" @default.
- W4360596391 modified "2023-10-14" @default.
- W4360596391 title "High-ordered spectral characterization of unicyclic graphs" @default.
- W4360596391 doi "https://doi.org/10.7151/dmgt.2489" @default.
- W4360596391 hasPublicationYear "2023" @default.
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