On mixed metric dimension of crystal cubic carbon structure

Abstract

Chemical graph theory is a branch of mathematical chemistry which applies classic graph theory to chemical phenomena and entities. Graphs are extensively used in chemistry to recognise the structures of chemical compounds, with the vertices and edges denoting atoms and bonds respectively. Let Γ = (V, E) be a nth order connected graph. If the distance vectors to the vertices in an ordered subset H r of vertices can uniquely identify each vertex of the graph Γ, then the set H r is known as resolving set for the graph Γ. The resolving set H r with smallest cardinality serves as the metric dimension of graph Γ and this resolving set serves as the metric basis for Γ. A unique representation of chemical structures can be obtained using a resolving set. In this manuscript, the most important variant of metric dimension known as mixed metric dimension is taken into consideration and computed it for most important allotrope of carbon commonly known as crystal cubic carbon.