Completely regular codes in the infinite hexagonal grid. (English) Zbl 1369.05061
Summary: A set \(C\) of vertices of a simple graph is called a completely regular code if for each \(i = 0, 1, 2, \dots\) and \(j = i - 1, i, i + 1\), all vertices at distance \(i\) from \(C\) have the same number \(s_{ij}\) of neighbors at distance \(j\) from \(C\). We characterize the completely regular codes in the infinite hexagonal grid graph.
MSC:
05C15 | Coloring of graphs and hypergraphs |
05C12 | Distance in graphs |
94C15 | Applications of graph theory to circuits and networks |
94B99 | Theory of error-correcting codes and error-detecting codes |