Reliabilities of chordal rings
X. D. Hu, F. K. Hwang · Networks · 1992
Abstract A chordal ring is a degree‐3 regular graph with n vertices on a ring and n/2 chords determined by a parameter h. Chordal rings are attractive as topologies for computer networks due to their simple structures and short diameters. In this work, we study the reliabilities of chordal rings assuming each edge can independently fail with probability p. For p small, the usual criterion to measure the reliability of a network is its line‐connectivity. We show that all chordal rings have the same line‐connectivity and the same super line‐connectivity. We analyze the reliabilities of chordal rings by using the recently developed notions of isolated and nonisolated cutsets and list the optimal choices of h for n ≤ 30.