Bilangan Kromatik Lokasi Amalgamasi Sisi Graf Lingkaran 𝒂𝒎𝒂𝒍𝒔(𝑪𝒏𝒋;𝒗𝒋,𝒍𝒗𝒋,𝒏) dengan 𝐧=𝟑,𝟒,𝟏≤𝐣≤𝐦, dan 𝐦≥𝟐

Abstrak

Let 𝐺 be a connected graph and П={𝑆1,𝑆2,…,𝑆𝑘} be an ordered partition of 𝑉(𝐺). Let 𝑆𝑖 is a set of color classes using colors 1,2,...,𝑘 where 𝑘 as positive integer. The color code 𝑐П(𝑣) of vertex 𝑣 in 𝐺 with respect to П is defined as 𝑘-vector, 𝑐П(𝑣)=(𝑑(𝑣,𝑆1),𝑑(𝑣,𝑆2),…,𝑑(𝑣,𝑆𝑖)) where 𝑑(𝑣,𝑆𝑖)=𝑚𝑖𝑛{𝑑(𝑣,𝑥)|𝑥∈𝑆𝑖} for 1≤𝑖≤𝑘. If each of vertices in 𝐺 have distinct color codes, then 𝑐 is called as locating coloring of 𝐺. The minimum number of colors that are used for locating coloring is called as locating chromatic number of 𝐺, denoted by 𝜒𝐿(𝐺). In this article we will discuss the chromatic number of the side amalgamation location of the circle graph 𝑎𝑚𝑎𝑙𝑠(𝐶𝑛𝑗;𝑣𝑗,𝑙𝑣𝑗,𝑛) with 𝑛=3,4,1≤𝑗≤𝑚, and 𝑚≥2.