METRIC DIMENSION OF FIBONACENE AND FULLERENE GRAPH - Ermawati Aribowo, Aghni
A hexagon is said to be linearly annelated if the hexagon is adjacent to exa- ctly two other hexagons and possesses two vertices of degree 2 which are not adjacent. A bonacene is a hexagonal chain without linearly annelated he- xagons. The name bonacene was proposed by Balaban in 1989. A graph appears from bonacenes is called a Fibonacene graph. Fullerene graphs is a graph that appears from fullerene molecule that was found by Kroto in 1985. A (k; 6)????fullerene graph is 3-regular planar that have faces size of k and 6 only. The possible value of k is 3,4, and 5. Let G be a connected graph with the vertices set V and the edges set E, distance between two vertices x and y is denoted by d(x; y). Let v 2 V;W V and W = fw1;w2; : : : ;wkg. The metric representation of vertex v with respect to W is dene as the k-tuple r(vjW) = (d(v;w1); d(v;w2) : : : ; d(v;wk)). The set W is said a resolving set for G if every two distinct vertices of G have distinct metric representations with respect to W. The metric dimension of graph G is the minimum cardi- nality of a resolving set for G. In this research we will compute the metric dimension of bonacene graphs with various types, namely Zigzag, Helicene and Serpent type. We also compute the metric dimension of some (3; 6)???? and (4; 6)????fullerene graphs.