BILANGAN KROMATIK LOKASI UNTUK GRAF AMALGAMASI BINTANG

Abstract

Let G = (V; E) be a connected graph and c a coloring of G. For i = 1; 2; :::; k,
we dene the color classes C
i
as the set of vertices receiving color i. The color code c
(v)
of a vertex v 2 V (G) is the k-vector (d(v; C
1
); d(v; C
2
); :::; d(v; C
k
)), where d(v; C
) is
the distance between v and C
. If all vertices of G have distinct color codes, then c is
called a locating-coloring of G. The locating-coloring number of graph G, denoted by

L
i
(G), is the smallest positive integer k such that G has a locating coloring with k color.
Let K
1;n
i
be star, where n
i
is the number of leaves of each star K
. We dene the
vertex amalgamation of star, denoted by S
k;(n
1
;:::;n
k
)
1;n
, as a graph obtained from stars
K
by identifying one arbitrary leaf from each star. We dene the edge amalgamation
of star, denoted by S
1;n
i

k;(n
, as a graph obtained by uniting an edge of each star.
If n
i
1
;:::;n
k
)
= m for each i, then we denoted the vertex amalgamation of star as S
and
the edge amalgamation of star as S

k;m
. In this paper we discuss the locating coloring of
S
k;(n
1
;:::;n
k
)
and S

k;(n
1
;:::;n
k
)
.