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Extremal Harary Index of Graphs with Given Number of Vertices of Odd Degree

Author

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  • Zhenhua Su
  • Zikai Tang
  • Hanyuan Deng
  • Meabed Khader

Abstract

The Harary index is one of the most investigated topological indices in mathematical chemistry and in related disciplines, which can be used to describe the molecular structure and physical properties. Let Gn,2k be the set of all connected graphs on n vertices with exactly 2k vertices of odd degree. Recently, the graphs in Gn,0 with the first four maximal Harary index and the first minimal Harary index are determined. In the paper, by using the edge-deleted method and some combinatorial skills, we characterize the graph in Gn,2k with the maximal Harary index for all 0≤k≤n/2, the graphs in Gn,2 with the first two minimal Harary index, and the graph in Gn,4 with the minimal Harary index. These results will be conducive to the further study of Harary index and its applications.

Suggested Citation

  • Zhenhua Su & Zikai Tang & Hanyuan Deng & Meabed Khader, 2022. "Extremal Harary Index of Graphs with Given Number of Vertices of Odd Degree," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-4, September.
    • Handle: RePEc:hin:jnlmpe:4916308
    DOI: 10.1155/2022/4916308
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