Abstract

In this paper, we examine the recently introduced concept of equidistant dimension $\mathrm{eqdim}(G)$ for Hamming graphs $H_{r,k}$. For hypercubes $Q_r=H_{r,2}$, exact values have been derived for \mbox{$r\not\equiv 0 (\!\!\!\mod 4)$}. Finally, the exact value for $\mathrm{eqdim}(H_{2,k})$ has been derived. We have shown that for Hamming graphs $H_{2,k}$, the equidistant dimension remains constant when $k\ge 5$, whereas for hypercubes, it grows linearly with the order of the graph.

Keywords: Distance-equalizer set; equidistant dimension; hypercubes; Hamming graphs.

MSC: 05C12, 05C69

DOI: 10.57016/MV-ZooS4049

Pages:  1--7