Modified Hourgand Graph Metric Dimensions

Abstract

For example, G is a connected graph and W is a subset of the set of points V on G. Set W is called the determining set on G if every point on G has different representations towards W. A determining set with a minimum number of members is called a minimum determining set or the basis of G and the cardinality of the minimum determinant set represents the metric dimension of the graph G. And denoted by dim(G). This paper discusses the metric dimensions of modified hourglass graphs mHgn constructed from a complete graph K1 with graphs Cn. Based on the results of the discussion, it was found that dim (mHgn) with m ≥ 3 and 3 ≤ n ≤ 5 is 2m.