On The Equitable Adjacent Strong Edge Colorings Of Some Graphs

Since lots of problems in the real world (such as drugs storage, the set-up of traffic lights, task arrangements and any other aspects) can be represented by the model of coloring graph, the relative theories of graphs and technique research has been always a hot topic in the area of graph theory. The development and application of modern information science and technology, computer science and technology, communication engineering as well as transportation engineering and the field of graph coloring has been constantly expanding. In connecting with graph coloring, besides the classical methods of point coloring and edge coloring, people proposed the dynamic coloring, conditions coloring, distance coloring, acyclic edge coloring, fractional coloring, adjacent strong edge coloring, equitable coloring and so on. The main content of this paper is the equitable adjacent strong edge coloring method of some graphs.The so-called equitable adjacent strong edge coloring of G is refers that based on the normal edge coloring edge coloring f in the graph, coloring meets the qualification of c(u)≠c(v) for any uv∈E(G), where c(u)={f(uv)|uv∈E(G)}, and the difference among the numbers of colors being used should be no more than 1. In this paper, by the aid of characteristics of some graphs, some correlative adjacent strong edge coloring problems were discussed, and the specific coloring programs have been provided. The main results are as follows:(1) The adjacent strong edge coloring numbers of wheel graph Wn, the ring graph Cn, the windmill graph K3t and graph Dm,n are respective as follows: (2) The equitable adjacent strong edge coloring numbers of the join graph of the empty graph and the path graph, the join graph of the star graph and the complete bipartite graph, and the generalizedθ-graph are respective as follows:...