Abstract
The field of graph theory is extensively used to investigate structure models in biology, computer programming, chemistry, and combinatorial optimization. In order to work with the chemical structure, chemists require a mathematical form of the compound. The chemical structure can be depicted using nodes (which represent the atom) and links (which represent the many types of bonds). As a result, a graph theoretic explanation of this problem is to give representations for the nodes of a graph such that different nodes have unique representations. This graph theoretic study is referred to as the metric dimension. In this article, we have computed the edge version of the metric dimension and doubly resolving sets for the family of cycle with chord C n t for n ≥ 6 and 2 ≤ t ≤ ⌊ n / 2 ⌋ .
Highlights
In research domains where networking is a basic and fundamental study block, graph theory is the most fundamental way to study and use these sciences
Several applications in chemical structure [4] and robot navigation [5] have been developed for the theoretical investigation of the metric dimension (MD). e MD of hamming graphs is linked to many coin weighing difficulties covered in [6, 7], as well as a detailed investigation of the game Mastermind given in [8]. is idea has been thoroughly investigated in a variety of domains, including combinatorial optimization [9], geographic routing protocols [10], and network discovery and verification [11]
The edge version of doubly resolving sets (EVDRSs) is used to find the upper bound of the edge version of metric dimension (EVMD) in the same manner as in the classical metric dimension case
Summary
Muhammad Ahmad ,1 Zohaib Zahid ,1 Tabasam Rashid ,1 and Juan Luis Garcia Guirao 2,3,4. E field of graph theory is extensively used to investigate structure models in biology, computer programming, chemistry, and combinatorial optimization. In order to work with the chemical structure, chemists require a mathematical form of the compound. E chemical structure can be depicted using nodes (which represent the atom) and links (which represent the many types of bonds). A graph theoretic explanation of this problem is to give representations for the nodes of a graph such that different nodes have unique representations. Is graph theoretic study is referred to as the metric dimension. We have computed the edge version of the metric dimension and doubly resolving sets for the family of cycle with chord Ctn for n ≥ 6 and 2 ≤ t ≤ ⌊n/2⌋
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