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Minimum Variable Connectivity Index of Trees of a Fixed Order

Author

Listed:
  • Shamaila Yousaf
  • Akhlaq Ahmad Bhatti
  • Akbar Ali

Abstract

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 is defined as , where is a nonnegative real number, is the edge set of , and denotes the degree of an arbitrary vertex in . 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 , 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 , where .

Suggested Citation

  • Shamaila Yousaf & Akhlaq Ahmad Bhatti & Akbar Ali, 2020. "Minimum Variable Connectivity Index of Trees of a Fixed Order," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-4, July.
    • Handle: RePEc:hin:jnddns:3976274
    DOI: 10.1155/2020/3976274
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