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Some Bounds on Randić Index of Graphs

Mobini, Melika | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55879 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Akbari, Saeed
  7. Abstract:
  8. In 1975 a Chemist Milan Randić proposed a concept named Randić index which is defined as follows: This index is generalized by replacing any real number α with which is called the general Randić index. Let G be a graph of order n. Erdős and Bollobás showed the lower bound for Randić index, Also, an upper bound for Randić index is n/2. In 2018 Suil O and Yongtang Shi proved a lower bound with minimum and maximum degree of a graph. They have shown for graph G we have, R(G) Also, a relation between Randić index and the energy of the graph has found. Indeed, it was proved that E(G) ⩾ 2R(G), where E(G) is the energy of graph. Many important bounds related to graph parameters for Randić index have been established such as the minimum degree, the chromatic number, the diameter, the radius, the average distance and eigenvalues.
  9. Keywords:
  10. Graph Energy ; Radius ; Diameter ; Eigen Values ; Chromatic Number ; Average Distance ; Randić index

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  • تعریف‌ها و نماد گذاری‌ها و قضایای ابتدایی
    • تعاریف و نمادگذاری‌های ابتدایی
    • قضیه‌ها و لم‌های ابتدایی
  • مهم‌ترین کران بالا و پایین برای شاخص رندیک
    • کران پایین
    • کران بالا
  • شاخص رندیک و پارامتر‌های دیگر گراف
    • شاخص رندیک و عدد رنگی
    • شاخص رندیک و کمر گراف
    • شاخص رندیک و شعاع گراف
    • شاخص رندیک، قطر و میانگین فاصله‌ی گراف
  • شاخص رندیک و انرژی گراف
  • برخی از نامساوی‌های شاخص رندیک
  • حدس‌ها
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  • واژه‌نامه فارسی به انگلیسی
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