Abstract
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.
Highlights
All graphs considered in this paper are finite undirected simple graphs
We study the cyclically interval total colorings of cycles and middle graphs of cycles
Since α is a cyclically interval total (2n −1) -coloring of coloring of M (Cn), we have
Summary
All graphs considered in this paper are finite undirected simple graphs. For a graph G, let V (G) and E (G) denote the set of vertices and edges of G, respectively. (2017) Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles. For any t ∈ , let Tt denote the set of graphs which have an interval total t
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