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 dG(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.
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