On Extremal Graphs of Degree Distance Index by Using Edge-Grafting Transformations Method

Muhammad Imran, Shehnaz Akhtar, Uzma Ahmad, Sarfraz Ahmad, Ahsan Bilal

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Background: Topological indices have numerous implementations in chemistry, biology and a lot of other areas. It is a real number associated with a graph, which provides information about its physical and chemical properties and their correlations. For a connected graph H, the degree distance DD index is defined as DD H = {h1,h2}v(H) degH h1 + degH h2 dH h1,h2, where degH h1 is the degree of vertex h1and dH h1,h2 is the distance between h1and h2in the graph H. Aim and Objective: In this article, we characterize some extremal trees with respect to degree distance index which has a lot of applications in theoretical and computational chemistry. Materials and Methods: A novel method of edge-grafting transformations is used. We discuss the behavior of DD index under four edge-grafting transformations Results: With the help of those transformations, we derive some extremal trees under certain parameters, including pendant vertices, diameter, matching and domination numbers. Some extremal trees for this graph invariant are also characterized. Conclusion: It is shown that balanced spider approaches to the smallest DD index among trees having given fixed leaves. The tree Cn,d has the smallest DD index, among all trees of diameter d. It is also proved that the matching number and domination numbers are equal for trees having a minimum DD index.

Original languageEnglish
Pages (from-to)560-567
Number of pages8
JournalCombinatorial Chemistry and High Throughput Screening
Issue number3
Publication statusPublished - Mar 2022


  • Degree distance index
  • Edge
  • Extremal graphs
  • Topological indices
  • Tree
  • Vertex

ASJC Scopus subject areas

  • Drug Discovery
  • Computer Science Applications
  • Organic Chemistry


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