Identity Graph of Finite Cyclic Groups
(1) Sanata Dharma University
(2) Sanata Dharma University
(3) Sanata Dharma University
(*) Corresponding Author
Abstract
This paper discusses how to express a finite group as a graph, specifically about the identity graph of a cyclic group. The term chosen for the graph is an identity graph, because it is the identity element of the group that holds the key in forming the identity graph. Through the identity graph, it can be seen which elements are inverse of themselves and other properties of the group. We will look for the characteristics of identity graph of the finite cyclic group, for both cases of odd and even order.
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A. Bretto, A. Faisant, L. Gilibert, G-graphs: A new representation of group, Journal of Symbolic Computation, 42, 549-560, 2007.
W. B. V. Kandasamy, F. Smarandache, Groups as Graphs. Slantina: Editura CuArt. 2009.
S. Lovett, Abstract Algebra. Boca Raton: CRC Press. 2016.
C. C. Miller, Essentials of Modern Algebra. Dulles, VA: Mercury Learning and Information, 2013.
R. Rajkumar, P. Devi, Coprime Graph of Subgroups of a Group, https://www.semanticscholar.org
M. U. Sherman-Bennett, On Groups and Their Graphs, MA: Bard College, 2016.
DOI: https://doi.org/10.24071/ijasst.v3i1.3256
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Publisher : Faculty of Science and Technology
Society/Institution : Sanata Dharma University
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