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Minimum Variable Connectivity Index of Trees of a Fixed Order
Joint Authors
Bhatti, Akhlaq Ahmad
Yousaf, Shamaila
Ali, Akbar
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-20
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
The connectivity index, introduced by the chemist Milan Randić in 1975, is one of the topological indices with many applications.
In the first quarter of 1990s, Randić proposed the variable connectivity index by extending the definition of the connectivity index.
The variable connectivity index for graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a nonnegative real number, EG is the edge set of G, and dt denotes the degree of an arbitrary vertex t in G.
Soon after the innovation of the variable connectivity index, its various chemical applications have been reported in different papers.
However, to the best of the authors’ knowledge, mathematical properties of the variable connectivity index, for γ>0, have not yet been discussed explicitly in any paper.
The main purpose of the present paper is to fill this gap by studying this topological index in a mathematical point of view.
More precisely, in this paper, we prove that the star graph has the minimum variable connectivity index among all trees of a fixed order n, where n≥4.
American Psychological Association (APA)
Yousaf, Shamaila& Bhatti, Akhlaq Ahmad& Ali, Akbar. 2020. Minimum Variable Connectivity Index of Trees of a Fixed Order. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-4.
https://search.emarefa.net/detail/BIM-1153016
Modern Language Association (MLA)
Yousaf, Shamaila…[et al.]. Minimum Variable Connectivity Index of Trees of a Fixed Order. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-4.
https://search.emarefa.net/detail/BIM-1153016
American Medical Association (AMA)
Yousaf, Shamaila& Bhatti, Akhlaq Ahmad& Ali, Akbar. Minimum Variable Connectivity Index of Trees of a Fixed Order. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-4.
https://search.emarefa.net/detail/BIM-1153016
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153016