A Research On The Coloring Of Expansion Graphs, Flows And Some Other Kinds Of Questions

The expansive structure of graphs and the theorems about chromatic orbit polynomials are researched in this paper. It is described that the chromatic orbit polynomials of maximum expansion graph of the regular polyhedrons and C60; and identified that infinite kinds of the expansion of the edge chromatic number of 3-regular and 3-edge colorable graphs. At the same time, it is found that the infinite kind of graphs which satisfy the Tutte's 4-flow conjecture. Finally, it is discussed that the k-arc transitive problem of Cayley graphs and vertex-transitive graph's s(mod k) cycle under the automorphism groups of graphs in this paper.