Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles

Abstract

A total coloring of a graph G is a function such 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.