Study to Formulate New Condition for a Graph to be Hamiltonian

Abstract

The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle within a graph is a simple cycle that passes through each vertex exactly once. The goal of our thesis was to find formula for a graph to be Hamiltonian. There is already a formula generated for a two cross over graph to be Hamiltonian. We are trying to find a condition for three cross over graph to be hamiltonian. First of this thesis provides scope and some literature reviews. The second gives preliminaries and sufficient condition for hamiltonicity. And the third gives some new condition of hamiltonian graph.