Identifying codes with small radius in some infinite regular graphs.
An edge coloring of a graph G with colors 1,2,...,t is called an interval t-coloring if for each i ∈ {1,2,...,t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable, if there is an integer t ≥ 1 for which G has an interval t-coloring. Let ℜ be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if G,H ∈ 𝔑, then the Cartesian product of these graphs...