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- W4308984300 abstract "A fundamental and challenging problem in spectral graph theory is to characterize which graphs are uniquely determined by their spectra. In Wang (2017), the author proved that an n-vertex graph G is uniquely determined by its generalized spectrum (DGS) whenever 2−⌊n2⌋detW is odd and square-free. Here, W is the walk matrix of G, namely, W=[e,Ae,…,An−1e] with e the all-one vector and A the adjacency matrix of G. In this paper, we focus on a larger family of graphs with dn square-free, where dn refers to the last invariant factor of W. We introduce a new kind of polynomial for a graph G associated with a prime p. Such a polynomial is invariant under generalized cospectrality. Using the newly defined polynomial, we obtain a sufficient condition for a graph in the larger family to be DGS. The main result of this paper improves upon the aforementioned result of Wang while the proof for the main result gives a new way to attack the problem of generalized spectral characterization of graphs." @default.
- W4308984300 created "2022-11-20" @default.
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- W4308984300 date "2023-02-01" @default.
- W4308984300 modified "2023-10-17" @default.
- W4308984300 title "An improved condition for a graph to be determined by its generalized spectrum" @default.
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- W4308984300 doi "https://doi.org/10.1016/j.ejc.2022.103638" @default.
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