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Journal of Applied Mathematics and Computing

Erschienen in:

21.05.2020 | Original Research

Comparative study of distance-based graph invariants

verfasst von: Hongzhuan Wang, Hongbo Hua, Maolin Wang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2020

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Abstract

The investigation on relationships between various graph invariants has received much attention over the past few decades, and some of these research are associated with Graffiti conjectures (Fajtlowicz and Waller in Congr Numer 60:187–197, 1987) or AutoGraphiX conjectures (Aouchiche et al. in: Liberti, Maculan (eds) Global optimization: from theory to implementation, Springer, New York, 2006). The reciprocal degree distance (RDD), the adjacent eccentric distance sum (AEDS), the average distance (AD) and the connective eccentricity index (CEI) are all distance-based graph invariants or topological indices, some of which found applications in Chemistry. In this paper, we investigate the relationship between RDD and other three graph invariants AEDS, CEI and AD. First, we prove that AEDS > RDD for any tree with at least three vertices. Then, we prove that RDD > CEI for all connected graphs with at least three vertices. Moreover, we prove that RDD > AD for all connected graphs with at least three vertices. As a consequence, we prove that AEDS > CEI and AEDS > AD for any tree with at least three vertices.

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Titel: Comparative study of distance-based graph invariants
verfasst von: Hongzhuan Wang
Hongbo Hua
Maolin Wang
Publikationsdatum: 21.05.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2020
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01363-2

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