BILANGAN KROMATIK LOKASI DARI GRAF P m P n ; K m P n ; DAN K , m K n

Abstract

Let G and H be two connected graphs. Let c be a vertex k-coloring of a
connected graph G and let = fC
g be a partition of V (G) into the resulting
color classes. For each v 2 V (G), the color code of v is dened to be k-vector: c
1
; C
2
; :::; C
k
(v) =
(d(v; C
1
); d(v; C
2
); :::; d(v; C
k
)), where d(v; C
i
) = minfd(v; x) j x 2 C
g, 1 i k. If
distinct vertices have distinct color codes with respect to , 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
)
are adjacent whenever a = a
0
and bb
0
2 E(H), or aa
0
i
2 E(G) and b = b
, denoted
by GH. 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.