The Locating Chromatic Number for Certain Operation of Origami Graphs

Abstract

The locating chromatic number introduced by Chartrand et al. in 2002 is the marriage of the partition dimension and graph coloring. The locating chromatic number depends on the minimum number of colors used in the locating coloring and the different color codes in vertices on the graph. There is no algorithm or theorem to determine the locating chromatic number of any graph carried out for each graph class or the resulting graph operation. This research is the development of scientific theory with a focus of the study on developing new ideas to determine the extent to which the locating chromatic number of a graph increases when applied to other operations. The locating chromatic number of the origami graph was obtained. The next exciting thing to know is locating chromatic number for certain operation of origami graphs. This paper discusses locating chromatic number for specific operation of origami graphs. The method used in this study is to determine the upper and lower bound of the locating chromatic number for certain operation of origami graphs. The result obtained is an increase of one color in the locating chromatic number of origami graphs.

The Locating Chromatic Number for the New Operation on Generalized Petersen Graphs N_P(m,1)

“…Furthermore, a methodology has been devised to calculate the locating chromatic number for origami graphs 𝑂 𝑚 and their divisions (one point on the outside of the edge) (Irawan et al, 2021). Subsequently (Asmiati et al, 2023) established the locating chromatic numbers for specific operations involving origami graphs.…”

The Locating Chromatic Number for Pizza Graphs

“…In this context, for each graph connected to G, since each coloring location is also a coloring (Harary & Melter, 1976). Operations of Origami Graphs (Asmiati et al, 2023) and edge amalgamation graphs of star graphs with order and complete graphs with order (Hartiansyah & Darmaji, 2023). From the description above, researchers are interested in exploring the chromatic number of locations on the pizza graph.…”