Christmas tree: A versatile 1-fault-tolerant design for token rings

Abstract

The token ring topology is required in token passing approach used in distributed operating systems. Fault tolerance is also required in the designs of distributed systems. Note that 1-fault-tolerant design for token rings is equivalent to design of 1-Hamiltonian graphs. This paper introduces a new family of graphs called Christmas tree, denoted by CT(s). The graph CT(s) is a 3-regular, planar, 1-Hamiltonian, and Hamiltonian-connected graph. The number of nodes in CT(s) is 3.2(s) - 2. Its diameter is 1 if s = 1, 3 if s = 2, and 2s if s greater than or equal to 3. (C) 1999 Elsevier Science B.V. All rights reserved.