Open Journal of Discrete Mathematics

Volume 7, Issue 4 (October 2017)

ISSN Print: 2161-7635   ISSN Online: 2161-7643

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Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles

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DOI: 10.4236/ojdm.2017.74018    675 Downloads   991 Views   Citations
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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.

Cite this paper

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.

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