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The fan graph is determined by its signless Laplacian spectrum

Muhuo Liu, Yuan Yuan, Kinkar Chandra Das (2020)

Czechoslovak Mathematical Journal

Given a graph G , if there is no nonisomorphic graph H such that G and H have the same signless Laplacian spectra, then we say that G is Q -DS. In this paper we show that every fan graph F n is Q -DS, where F n = K 1 P n - 1 and n 3 .

The Gerschgorin discs under unitary similarity

Anna Zalewska-Mitura, Jaroslav Zemánek (1997)

Banach Center Publications

The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.

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