Bounds and extremal graphs of second reformulated Zagreb index for graphs with cyclomatic number at most three
Joint Authors
Rajpoot, Abhay
Selvaganesh, Lavanya
Source
Issue
Vol. 49, Issue 1 (31 Jan. 2022), pp.1-21, 21 p.
Publisher
Kuwait University Academic Publication Council
Publication Date
2022-01-31
Country of Publication
Kuwait
No. of Pages
21
Main Subjects
Abstract EN
Mili\v{c}evi\'{c} \textit{et al.}, in 2004, introduced topological indices known as Reformulated Zagreb indices, where they modified Zagreb indices using the edge-degree instead of vertex degree.
In this paper, we present a simple approach to find the upper and lower bounds of the second reformulated Zagreb index, $EM_2(G)$, by using six graph operations/transformations.
We prove that these operations significantly alter the value of reformulated Zagreb index.
We apply these transformations and identify those graphs with cyclomatic number at most 3, namely trees, unicyclic, bicyclic and tricyclic graphs, which attain the upper and lower bounds of second reformulated Zagreb index for graphs.
American Psychological Association (APA)
Rajpoot, Abhay& Selvaganesh, Lavanya. 2022. Bounds and extremal graphs of second reformulated Zagreb index for graphs with cyclomatic number at most three. Kuwait Journal of Science،Vol. 49, no. 1, pp.1-21.
https://search.emarefa.net/detail/BIM-1500060
Modern Language Association (MLA)
Rajpoot, Abhay& Selvaganesh, Lavanya. Bounds and extremal graphs of second reformulated Zagreb index for graphs with cyclomatic number at most three. Kuwait Journal of Science Vol. 49, no. 1 (Jan. 2022), pp.1-21.
https://search.emarefa.net/detail/BIM-1500060
American Medical Association (AMA)
Rajpoot, Abhay& Selvaganesh, Lavanya. Bounds and extremal graphs of second reformulated Zagreb index for graphs with cyclomatic number at most three. Kuwait Journal of Science. 2022. Vol. 49, no. 1, pp.1-21.
https://search.emarefa.net/detail/BIM-1500060
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 19-21
Record ID
BIM-1500060