Optimal Fault-Tolerant Hamiltonian and Hamiltonian Connected Graphs

Abstract

A k-regular hamiltonian and hamiltonian connected graph G is optimal fault-tolerant hamiltonian and hamiltonian connected if G remains hamiltonian after removing at most k - 2 nodes and/or edges and remains hamiltonian connected after removing at most k - 3 nodes and/or edges. In this paper, we investigate a construction scheme to construct optimal fault-tolerant hamiltonian and hamiltonian connected graphs. Hence, some of the generalized hypercubes, Twisted-cubes, Crossed-cubes, and Mobius cubes are optimal fault-tolerant hamiltonian and optimal fault-tolerant hamiltonian connected.