Hamilton Cycle on the Wheel Graph

This article discusses the existence of the Hamilton cycle in the wheel graph by constructing steps to find the existence of the Hamilton cycle. A graph that has a Hamilton cycle is called a Hamilton graph, A circle graph is a graph where each vertex has a degree of two, denoted by Cn. A graph obtained by adding a central vertex to a circle graph and connecting it to all the vertices of the circle graph is called a wheel graph, denoted by Wn . If the wheel graph Wn has m where m is the number of that replaces each point in Wn then it can be denoted by Wmn . Then, in the wheel graph Wmn is the number of outermost points of Wmn added to 1 point located in the center. Based on the construction, it is found that there is a Hamilton cycle in the wheel graph. In the wheel graph Wn contains Hamilton cycle for n>=3. Furthermore, the wheel graph Wmn also contains Hamilton cycle for n>=3 and m>=1, but the image of the wheel graph Wmn is only perfectly drawn for n=2k where k is an integer. This is because there are colliding edges in the wheel graph for n=2k-1 where k is an integer.