Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

Abstract

Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

Mathematical analysis of the structure of one-heptagonal carbon nanocone in terms of its basis and dimension

“…The computation of metric dimension for molecular graph families is always a challenging task because deciding/selecting landmark vertices (atoms) in minimum numbers is not that easy due to the complexity and scalability of the structures [30]. Although, several authors studied metric dimension and its related variants for several distinct complex molecular graphs as well as for various other graph-theoretic aspects, for example, the metric dimension of H-Napthalenic nanotubes as well as VC 5 C 7 were investigated in [32]; edge metric basis and the dimension of one-pentagonal and one-heptagonal carbon nanocone was investigated [9,20] respectively; for cellulose networks an estimated upper bounds were provided for the cardinality of their resolving sets [33]; the metric dimension of Alpha & 2D lattice boron nanotubes were reported [34]; for polycyclic aromatic hydrocarbons several variants of metric dimension were investigated [35,36]; for chemical graphs of starphene and hollow coronoid several metric dimension variants were reported [37][38][39]. For certain chemical as well as planar graphs, these variants are investigated [20,27,28].…”

Multiset and Mixed Metric Dimension for Starphene and Zigzag-Edge Coronoid

“…1, denoted by HC a,b,c , can be considered as a structure formed by fusing six linear polyacenes segments into a closed loop. A hollow coronoid [19] is another name for this structure. It is classified as catacondensed coronoids, and it belongs to the primitive coronoids sub-cluster [7].…”

“…In this paper we not only compute mixed metric dimension of studied graph but also compare the results with the metric and edge metric dimension. Koam et al [19], recently studied the vertex and edge resolvability for hollow coronoid HC a,b,c . They proved that HC a,b,c is the family of plane graphs with the constant vertex and edge metric dimension(EMD).…”

Edge based metric dimension of various coffee compounds

“…They proved that edge metric dimension of all the chosen structures is constant. Edge and its fault-tolerant version of metric dimension are studied in [ 30 ], they studied these parameters for the hollow coronoid structures. Similarly, all the resolvability parameters for the benzenoid tripod structure are found in [ 31 ].…”