Modular Chromatic Number of Some Unicyclic Graphs

• Main Author: NOOR FAIZAH (NIM: 90113002), PUJI
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/20408
• Institution: Institut Teknologi Bandung

The modular coloring in graph was introduced by Futaba Okamoto, Ebrahim Salehi and Ping Zhang in 2009. For k ≥ 2, a modular –k coloring of a graph G without isolated vertices is a coloring of the vertices of G with the elements in Zk (where adjacent vertices may be colored by the same color) having the property that for every two adjacent vertices of G , the sums of the colors of their neighbors are different in Zk . The modular chromatic number mc (G) of is the minimum for which has a modular k-coloring. The modular chromatic number of a graph is at least the same as its chromatic number. The objective of this thesis is to determine the modular chromatic number of some unicyclic graphs, obtained by operation a cycle with stars, a cycle with a path and a star, and a cycle with paths.