Supported by the NNSF of China(Grant No.11761064,61163037)
Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to b...
Supported by the NNSF of China(10861009);Supported by the Ministry of Education Science and Technology Item of China(206156)
By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph(the Theorem 1), a first class hi-cycle graph and a second class bicycle graph...