Extremal k-generalized quasi trees for general sum-connectivity index

Muhammad Kamran Jamil, Ioan Tomescu, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

For a simple graph G, the general sum-connectivity index is defined as χα(G) = ∑uvE(G) (d(u) + d(v))α, where d(u) is the degree of the vertex u and α ≠ 0 is a real number. The k-generalized quasi tree is a connected graph G with a subset Vk ⊂ V (G), where |Vk | = k such that G − Vk is a tree, but for any subset Vk−1 ⊂ V (G) with cardinality k − 1, G − Vk−1 is not a tree. In this paper, we have determined sharp upper and lower bounds of the general sum-connectivity index for α ≥ 1. The corresponding extremal k-generalized quasi trees are also characterized in each case.

Original languageEnglish
Pages (from-to)101-106
Number of pages6
JournalUPB Scientific Bulletin, Series A: Applied Mathematics and Physics
Volume82
Issue number2
Publication statusPublished - 2020

Keywords

  • Extremal graphs
  • General sum-connectivity index
  • K-quasi trees

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Applied Mathematics

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