Research On The Some Topics Of Graph Theory

This paper which stands on the basis of previous results, do further research on hamiltonian and one of the special case of Vizing's conjecture.●In the first two sections, we introduce the background and significance of the research, including the development of a representative at home and abroad regarding this aspect. Based on this research background and profound dis-cussion, it fully shows the main work's necessity and innovation.●In Section 3, we study the properties of the longest cycle which is also a dom-inating cycle. After that, we show a new sufficient condition for Hamiltonian.●In Section 4, in the 3-edge-chromatic critical graph, a new bound for the independence number are given.