Research on the Hamiltonicity and Its Classifications Concerning Cubic Graphs of Order 8

Abstract

A cubic graph is a 3-regular graph. Peterson graph, a famous graph in graph theory, is a cubic graph of order 10. In this paper, the idea about the concyclic points is introduced. To utilize the idea of the concyclic points, we have divided all the cubic graphs, the order of which is 8, into 5 categories. We prove that the connected cubic graph of order 8 is just right the five categories discussed above, up to isomorphism. Hence, a connected cubic graph of order 8 is a Hamiltonian graph. At the end of the article, some properties and characteristics about cubic graph of order 8 are given.