Note on Cyclically Interval Edge Colorings of Simple Cycles

Abstract

A proper edge t -coloring of a graph G is a coloring of its edges with colors 1, 2,..., t , such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t -coloring of a graph G is a proper edge t -coloring of G such that for each vertex , either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. In this paper, we provide a new proof of the result on the colors in cyclically interval edge colorings of simple cycles which was first proved by Rafayel R. Kamalian in the paper “On a Number of Colors in Cyclically Interval Edge Colorings of Simple Cycles, Open Journal of Discrete Mathematics , 2013, 43-48”.