Exploring the Strong Metric Dimension of Hollow Coronoid Structures: Applications and Implications
Keywords:
metric, metric dimension, strong metric dimension, strong resolving graph, vertex cover numberAbstract
Coronoid systems are actually geometric arrangements of six-sided benzenoids in hexagonal form. Coronoid systems are organic chemical structures, that fall into two categories: primitive and catacondensed
coronoids. Many researchers from various fields have an interest in the mathematical analysis of chemicals. Graph theory played an important role in studying chemical structures by transforming them into a graph. The strongιmetricιdimension is one of the main parameter ofιgraph theory. Consider a connectedιgraphιG, aιvertexιu strongly resolves aιpairι(x, y) of vertices if either x lies onιaιshortestιpathιbetween u - y or y lies onιaιshortestιpathιbetween u - x. The setιS is referred as theιstrong resolving set ofιG if any vertex in S can strongly resolve every pair of distinct vertices in G.ιThe minimumιcardinality of such set S is known as the strong metricιdimension ofιG.
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