This paper studies routing vulnerability in networks modeled by chordal ring graphs. In a chordal ring graph, the vertices are labeled in2n and each even vertex i is adjacent to the vertices i + a, i + b, i, + c, where a, b, and c are different odd integers. Our study is based on a geometrical representation that associates to the graph a tile which periodically tessellates the plane. Using this approach, we present some previous results on triple-loop graphs, including an algorithm to calculate the coordinates of a given vertex in the tile. Then, an optimal consistent fault-tolerant routing of shortest paths is defined for a chordal ring graph with odd diameter and maximum order. This is accomplished by associating to the chordal ring graph a triple-loop one. When some faulty elements are present in the network, we give a method to obtain central vertices, which are vertices that can be used to reroute any communication affected by the faulty elements. This implies that the diameter of the corresponding surviving route graph is optimum.
