Counting the Numbers of Paths of All Lengths in Symmetric Dendrimers and Its Applications

Journal article

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Computational Science and Engineering (Digital Transformation)

Publication Details

Author list: Tabassum, Hafsah; Ul Haq Bokhary, Syed Ahtsham; Jiarasuksakun, Thiradet; Kaemawichanurat, Pawaton;

Publication year: 2022

Volume number: 88

Issue number: 3

Start page: 659

End page: 681

Number of pages: 23

ISSN: 03406253

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85129518601&doi=10.46793%2fmatch.88-3.659T&partnerID=40&md5=94d60390eb14360c4d582a81d4067eb4

Languages: English-Great Britain (EN-GB)

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Abstract

The dendrimers are highly branched organic macromolecules having repeated iterations of branched units that surrounds the central core. Dendrimers are used in a variety of fields including chemistry, nanotechnology and biology. For positive integers n and k, the symmetric dendrimer Tn,k is defined as the rooted tree of radius n whose all vertices at distance less than n from the root have degree k and all pendent vertices have equal distance n from the root. In this paper, for any positive integer ℓ, we count the number of paths of length ℓ of Tn,k. As a consequence of our main results, we obtain the average distance of Tn,k which we can establish an alternate proof for the Wiener index of Tn,k. Further, we generalize the concept of medium domination, introduced by Vargör and Dündar in 2011, of Tn,k © 2022 University of Kragujevac, Faculty of Science. All rights reserved.

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