Some Bounds on Randić Index of Graphs

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Mobini, Melika | 2023

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55879 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saeed
Abstract:
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.
Keywords:
Graph Energy ; Radius ; Diameter ; Eigen Values ; Chromatic Number ; Average Distance ; Randić index