Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups

Walter Klotz, Torsten Sander

Abstract


It is shown that distance powers of an integral Cayley graph over an abelian group $\Gamma$ are again integral Cayley graphs over $\Gamma$. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum.

Keywords


Cayley graphs; Graph eigenvalues; Distance powers

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