Christmas tree: a 1-fault-tolerant network for token rings

The token ring topology is required in the token passing approach used in distributed operating systems. Fault tolerance is also required in the design of distributed systems. We consider the 1-fault-tolerant design for token rings, which can tolerate 1-processor fault- or 1-link fault. Note that the 1-fault-tolerant design for token rings is equivalent to the design of 1-Hamiltonian graphs. The paper introduces a new family of interconnection networks called Christmas tree. The under graph of the Christmas tree, denoted by CT(s), is a 3-regular, planar, 1-Hamiltonian, and Hamiltonian-connected graph. The number of nodes and the diameter of CT(s) are 3×2^s-2 and 2s, respectively. In other words, the diameter of CT(s) is 2 log₂ n-O(1), where n is the number of nodes