THE METRIC DIMENSION OF A GRAPH COMPOSITION PRODUCTS WITH STAR
Abstract: A set of vertices W
resolves a graph G if every vertex is uniquely determined by its coordinate of
distances to the vertices in W . The minimumcardinality of a resolving set of G
is called the metric dimension of G. In thispaper, we consider a graph which is
obtained by the composition product betweentwo graphs. The composition product
of graphs G and H, denoted by G[H], is the graph with vertex set V (G) × V (H)
= f(a; v)ja 2 V (G); v 2 V (H)g, where (a; v)adjacent with (b; w) whenever ab 2
E(G), or a = b and vw 2 E(H). We give ageneral bound of the metric dimension of
a composition product of any connectedgraph G and a star. We also show that the
bound is sharp.
Author: S.W. Saputro, D.
Suprijanto, E.T. Baskoro , and A.N.M. Salman
Journal Code: jpmatematikagg120019
