On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs

Abeer M. Albalahi, Akbar Ali and Efthymios G. Tsionas

Journal of Mathematics, 2022, vol. 2022, 1-6

Abstract: Let G be a graph. Denote by du, the degree of a vertex u of G and represent by vw, the edge of G with the end-vertices v and w. The sum of the quantities du2+dv2du−1dv−1 over all edges uv of G is known as the symmetric division deg (SDD) index of G. A connected graph with n vertices and n−1+k edges is known as a (connected)k-cyclic graph. One of the results proved in this study is that the graph possessing the largest SDD index over the class of all connectedk-cyclic graphs of a fixed order n must have the maximum degree n−1. By utilizing this result, the graphs attaining the largest SDD index over the aforementioned class of graphs are determined for every k=0,1,…,5. Although, the deduced results, for k=0,1,2, are already known, however, they are proved here in a shorter and an alternative way. Also, the deduced results, for k=3,4,5, are new, and they provide answers to two open questions posed in the literature.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/7783128.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/7783128.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7783128

DOI: 10.1155/2022/7783128

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().