Resolving Share and Topological Index

2014/08/01 by Muhammad Salman, Salman, Muhammad, Imran Javaid +3 · 2 citations
Computer Science · Mathematics · #Computational Drug Discovery Methods #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO #msc:05C12

paper · pdf · doi:10.48550/arxiv.1408.0132

16 pages, 2 figures

arxiv created 2014/08/01 · arxiv updated 2014/08/04

Abstract

An atom a of a molecular graph G uniquely determines (resolves) a pair (a₁,a₂) of atoms of G if the distance between a and a₁ is different from the distance between a and a₂. In this paper, we quantify the involvement of each atom a of G in uniquely determining (resolving) a pair (a₁,a₂) of atoms of G, which is called the resolving share of a for the pair (a₁,a₂). Using this quantity, we define a distance-based topological index of a molecular graph, which reflects the topology of that molecular graph according to the resolvability behavior of each of its atom, and is called the resolving topological index. Then we compute the resolving topological index of several molecular graphs.

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