New resolvability parameters of graphs
In this paper we introduce two concepts related to resolvability and the metric dimension of graphs. The kth dimension of a graph G is the maximum cardinality of a subset of vertices of G that is resolved by a set S of order k. Some first results are obtained. A pair of vertices u, v is totally resolved by a third vertex x if (Formula presented.) A total resolving set in G is a set S such that each pair of vertices of G is totally resolved be a vertex in S. The total metric dimension of a graph is the minimum cardinality of a total resolving set. We determine the total metric dimension of paths, cycles, and grids, and of the 3-cube, and the Petersen graph.
|AKCE International Journal of Graphs and Combinatorics|
Hedetniemi, S.T. (Stephen T.), Laskar, R.C, & Mulder, H.M. (2020). New resolvability parameters of graphs. AKCE International Journal of Graphs and Combinatorics. doi:10.1016/j.akcej.2019.12.021