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

TL;DR

This paper proves that distance powers and distance matrices of integral Cayley graphs over abelian groups retain integrality, highlighting their spectral properties and structural stability.

Contribution

It establishes that distance powers of integral Cayley graphs over abelian groups are also integral Cayley graphs, and their distance matrices have integral spectra.

Findings

Distance powers of integral Cayley graphs are integral Cayley graphs.

Distance matrices of these graphs have integral spectra.

Structural stability of integrality under distance operations.

Abstract

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