Addresses for graphs

The problem of labeling the vertices of an undirected, connected graph with binary -tuple addresses is considered. These addresses are to have the property that if two vertices are a distance apart in the graph then the Hamming distance between the corresponding addresses must be where is a positive integer which is constant for the graph. Not all graphs may be so addressed. A weak characterization of addressable graphs in terms of the eigenvalues of a certain matrix associated with the graph is given. It is shown that any addressable bipartite graph may always be addressed with . For nonbipartite addressable graphs, must be even, and it is shown that there exist graphs requiring an arbitrarily large for addressing. An addressing algorithm is given which is guaranteed to address any addressable graph.