Zai, N. A. F. O. and Sarmin, N. H. and Khasraw, S. M. S. and Gambo, I. and Zaid, N. (2021) The nonzero divisor graph of ring of integers modulo six and the hamiltonian quaternion over integers modulo two. In: 28th Simposium Kebangsaan Sains Matematik, SKSM 2021, 28 July 2021  29 July 2021, Kuantan, Pahang, Virtual.

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Official URL: http://dx.doi.org/10.1088/17426596/1988/1/012074
Abstract
The study of graph theory was introduced and widely researched since many practical problems can be represented by graphs. A nonzero divisor graph is a graph in which its set of vertices is the nonzero elements of the ring and the vertices x and y are adjacent if and only if xy ≠ 0. In this study, we introduced the nonzero divisor graphs of some finite commutative rings in specific the ring of in tegers modulo 6, 6 and ring of Hamiltonian quaternion, (2). First, the nonzero divisors of the commutative rings are found. Then, the nonzero divisor graphs are constructed. Finally, some properties of the graph, including the chromatic number, clique number, girth and the diameter are obtained.
Item Type:  Conference or Workshop Item (Paper) 

Uncontrolled Keywords:  chromatic number, clique number, commutative ring 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  95672 
Deposited By:  Narimah Nawil 
Deposited On:  31 May 2022 13:04 
Last Modified:  31 May 2022 13:04 
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