Minimum Metric Dimension of Silicate Networks

Paul Manuel1,2, Indra Rajasingh2
1Department of Information Science, Kuwait University, Kuwait 13060
2Department of Mathematics, Loyola College, Chennai, India 600 034

Abstract

The silicates are the largest, the most interesting and the most complicated class of minerals by far. The basic chemical unit of silicates is the \((\text{SiO}_4)\) tetrahedron. A silicate sheet is a ring of tetrahedrons which are linked by shared oxygen nodes to other rings in a two-dimensional plane that produces a sheet-like structure. We consider the silicate sheet as a fixed interconnection parallel architecture and call it a silicate network. We solve the Minimum Metric Dimension problem, which is NP-complete for general graphs.