Author(s)

Yongqiang Zhao¹, Shijun Su²

¹School of Science, Shijiazhuang University, Shijiazhuang, China.
²School of Science, Hebei University of Technology, Tianjin, China.

A total coloring of a graph G is a functionsuch that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. A k-interval is a set of k consecutive integers. A cyclically interval total t-coloring of a graph G is a total coloring a of G with colors 1,2,...,t, such that at least one vertex or edge of G is colored by i,i=1,2,...,t, and for any, the set is a -interval, or is a -interval, where d_G(x) is the degree of the vertex x in G. In this paper, we study the cyclically interval total colorings of cycles and middle graphs of cycles.

Total Coloring, Interval Total Coloring, Cyclically Interval Total Coloring, Cycle, Middle Graph

Zhao, Y. and Su, S. (2017) Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles. Open Journal of Discrete Mathematics, 7, 200-217. doi: 10.4236/ojdm.2017.74018.