International Journal of Mathematics Trends and Technology
Volume 65 | Issue 6 | Year 2019 | Article Id. IJMTT-V65I6P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I6P511
A.Manisekar, A.Mageswari, M.V.Suresh, "Some Results On Power Graph Of Finite Cyclic Group," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 6, pp. 67-70, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I6P511
Let be a group. The power graph (𝐺) of G is a graph with vertex set V(𝑃(𝐺)) = 𝐺 and two distinct vertices x and y are adjacent in 𝑃(𝐺) if and only if either 𝑥𝑖 = 𝑦 or 𝑦𝑗 = 𝑥, where 2 ≤ 𝑖, 𝑗 ≤ 𝑛. We discuss some graph theoretical properties of power graph for some classes of finite cyclic group. Further we discuss some domination parameters of power graph for some classes of finite cyclic group.
[1] Abdollahi, S. Akbari and H.R. Maimani, Non-Commuting graph of a group, J. Algebra, 298, 68-492, 2006.
[2] S. Akbari and A. Mohammadian, On the zero-divisor graph of commutative ring, J.Algebra, 274 (2), 847-855 ,2004.
[3]D.Alireza, E. Ahmad and J. Abbas, Some results on the power graphs of finite groups, Scienceasia 41, 73-78 ,2015, doi:10.2306/scienceasia15131874.2015.41.073.
[4] Cameron PJ (2010) The power graph of a finite group II. J Group Theor13, 779–83 ,2010.
[5] I. Chakrabarty, S. Ghosh and M.K. Sen, Undirected power graphs of semi groups, Semi group Forum,78,2009, 410-426.
[6] M. Mirzargar, A. R. Ashra and M. J. Nadjafi-Arani, On the power graph of a finite group, Filomat, 26 (6), 1201-1208 ,2012.
[7] T. TamizhChelvam and M. Sattanathan, Power graph of finite abelian groups, Algebra and Discrete Mathematics, 16 , 33-41 ,2013.
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