Modular Chromatic Number of Certain Cyclic Graphs

Abstract

A modular - coloring,  of a graph without isolated vertices is vertex coloring of  with the positive integers , for all  , where the adjacent vertices may be colored by the same integer and sums of the colors of their neighbors are different in . The minimum  for which the  has a modular - coloring is the modular chromatic number  of   . In this paper, the modular chromatic number of generalized Jahangir graph, generalized Petersen graph, and generalized uniform theta graph are found.