Dimensi Metrik Graf Buckminsterfullerene-Subdivisi dan Buckminsterfullerene-Star

Misalkan terdapat graf Buckminsterfullerene  dengan 60 titik. Graf Buckminsterfullerene-subdivisi, dinotasikan , , dikonstruksi dengan cara melakukan operasi subdivisi terhadap satu sisi tertentu di , yaitu penyisipan sebanyak  titik di sisi tersebut. Selanjutnya, Graf Buckminsterfullerene-star, dinotasikan , dikonstruksi dengan cara mengidentifikasi masing-masing satu titik daun dari lima graf bintang  dengan titik yang bersesuaian di Pada artikel ini akan ditentukan dimensi metrik dari dan  untuk

On the Metric Dimension for Snowflake Graph

The concept of metric dimension is derived from the resolving set of a graph, that is measure the diameter among vertices in a graph. For its usefulness in diverse fields, it is interesting to find the metric dimension of various classes of graphs. In this paper, we introduce two new graphs, namely snowflake graph and generalized snowflake graph. After we construct these graphs, aided with a lemma about the lower bound of the metric dimension on a graph that has leaves, and manually recognized the pattern, we found that dim(Snow) = 24 and dim(Snow(n,a,b,c)) = n(a+c+1)

Metric dimension of fullerene graphs

A resolving set W is a set of vertices of a graph G(V, E) such that for every pair of distinct vertices u, v ∈ V(G), there exists a vertex w ∈ W satisfying d(u, w) ≠ d(v, w). A resolving set with minimum number of vertices is called metric basis of G. The metric dimension of G, denoted by dim(G), is the minimum cardinality of a resolving set of G. In this paper, we consider (3, 6)-fullerene and (4, 6)-fullerene graphs and compute the metric dimension for these fullerene graphs. We also give conjecture on the metric dimension of (3, 6)-fullerene and (4, 6)-fullerene graphs.</p