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Comparative study of distance-based graph invariants

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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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Acknowledgements

The first author was supported by National Natural Science Foundation of China under Grant Nos. 11971011 and 11571135. The second author was supported by National Natural Science Foundation of China under Grant Nos. 11971011,11571135 and Qing Lan Project of Jiangsu Province, P.R. China.

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  1. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an City, 223003, People’s Republic of China

    Hongzhuan Wang, Hongbo Hua & Maolin Wang

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  1. Hongzhuan Wang
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  2. Hongbo Hua
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  3. Maolin Wang
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Correspondence to Hongbo Hua.

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Wang, H., Hua, H. & Wang, M. Comparative study of distance-based graph invariants. J. Appl. Math. Comput. 64, 457–469 (2020). https://doi.org/10.1007/s12190-020-01363-2

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  • DOI: https://doi.org/10.1007/s12190-020-01363-2

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