BILANGAN KROMATIK LOKASI DARI GRAF Pm â–¡ Pn, Km â–¡ Pn, DAN Kmâ–¡ Kn
Abstract: Let G and H be two
connected graphs. Let c be a vertex k-coloring of a connected graph G and let
II = {C1,C2, ..., Ck} be a partition of V (G) into the resulting color classes.
For each ðœ ϵ V (G), the color code of ðœ is
defined to be k-vector: cII(ðœ) = (d(ðœ,C1), d(ðœ,C2), ..., d(ðœ,Ck)),
where d(ðœ,Ci) = min{d(ðœ, x) | x
ϵ Ci}, 1 ≤ i ≤ k. If distinct vertices have distinct color
codes with respect to II, then c is called a locating coloring of G. The
locating chromatic number of G is the smallest natural number k such that there
are locating coloring with k colors in G. The Cartesian product of graph G and
H is a graph with vertex set V (G) × V (H), where two vertices (a, b) and (a',
b') are adjacent whenever a = a' and bb' ϵ (H), or aa' ϵ E(G) and b = b',
denoted by Gâ–¡H. In this paper, we will study about the locating
chromatic numbers of the cartesian product of two paths, the cartesian product
of paths and complete graphs, and the cartesian product of two complete graphs.
Penulis: MARIZA WENNI
Kode Jurnal: jpmatematikadd130100
