Some properties of graphs associated with certain finite rings / Wan Muhammad Afif Wan Ruzali

Wan Muhammad Afif, Wan Ruzali (2019) Some properties of graphs associated with certain finite rings / Wan Muhammad Afif Wan Ruzali. Masters thesis, University of Malaya.

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      Abstract

      In this thesis, we investigate the properties of some graphs associated with finite rings, namely the total graphs, the unit graphs, and the directed graphs (also called digraphs). We start by describing the structure of the total graphs and unit graphs of some rings, particularly those of order p, p2 and pq where p and q are distinct primes. This involves computing the degrees of vertices and the number of connected components in those graphs. We also obtain explicit formulae for determining the number of sources or non-sources in the digraphs of certain rings. of special importance is the result related to the digraph associated with the ring of integers modulo pn, which is then used to extend the result on the number of sources to include the digraph associated with the more general ring Zn. Some graph parameters concerning the digraph associated with the ring I = ha, b : pa = pb = 0, a2 = b, ab = 0i of order p2 are also obtained, including the number of non-sources, the number of connected components, and the number of vertices in each connected component.

      Item Type: Thesis (Masters)
      Additional Information: Dissertation (M.A.) – Faculty of Science, University of Malaya, 2019.
      Uncontrolled Keywords: Finite ring; Total graph; Unit graph; Directed graph; Zero divisor
      Subjects: Q Science > Q Science (General)
      Q Science > QA Mathematics
      Divisions: Faculty of Science
      Depositing User: Mr Mohd Safri Tahir
      Date Deposited: 20 Feb 2020 08:41
      Last Modified: 17 Aug 2020 08:09
      URI: http://studentsrepo.um.edu.my/id/eprint/11052

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