Cyclically Interval Total Coloring of the One Point Union of Cycles

Abstract

A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union  of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles  and  are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.