Computing Edge Version of Resolvability and Double Resolvability of a Graph

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 ⌋ .

Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters

“…Nullity is expressed in terms of maximum degree of a vertex [22] , [23] . Authors of [24] , [25] , computed the double metric resolvability of convex polytopes, authors of [26] , computed the edge version of resolvability and double resolvability of some generalized graphs.…”

Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph

“…For the first time, Chen et al explicitly approximated the upper and lower bounds for the MDRS problem [28]. In [29], the minimal resolving sets and DMD of the line graph of chorded cycles were examined. Authors demonstrated that the DMD of L(C t n ) is exactly one greater than its MD.…”

Double Metric Resolvability in Convex Polytopes

“…For the layer-sun graphs and their related line graphs, the MDRS problem was also studied in [37]. In [38], the minimal resolving sets and DMD of the line graph of chorded cycles were examined. Authors demonstrated that the DMD of L(C t n ) is exactly one greater than its MD.…”