Abstract:We study various spectral properties of the Seidel matrix S of a connected chain graph. We prove that −1 is always an eigenvalue of S and all other eigenvalues of S can have multiplicity at most two. We obtain the multiplicity of the Seidel eigenvalue −1, minimum number of distinct eigenvalues, eigenvalue bounds, characteristic polynomial, lower and upper bounds of Seidel energy of a chain graph. It is also shown that the energy bounds obtained here work better than the bounds conjectured by Haemers. We also o… Show more
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