On mixed metric dimension of crystal cubic carbon structure

Document Type

Article

Publication Title

Journal of Mathematical Chemistry

Abstract

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 Hr of vertices can uniquely identify each vertex of the graph Γ , then the set Hr is known as resolving set for the graph Γ . The resolving set Hr with smallest cardinality serves as the metric basis for Γ and this cardinality of the metric basis set is termed as the metric dimension of 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. Graphical abstract: Mixed metric dimension of Crystal Cubic Carbon structure has been computed and a comparison among metric dimension, edge metric dimension and mixed metric dimension has been done, from which we find that these three dimensions are equal.[Figure not available: see fulltext.]

First Page

2079

Last Page

2097

DOI

10.1007/s10910-023-01507-2

Publication Date

11-1-2023

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