Abstract:
Let $ {E}_{n} $ be the ring of Eisenstein integers modulo $n$. We denote by $G({E}_{n})$ and $G_{{E}_{n}}$, the unit graph and the unitary Cayley graph of $ {E}_{n} $, respectively. In this paper, we obtain the value of the diameter, the girth, the clique number and the chromatic number of these graphs. We also prove that for each $n>1$, the graphs $G(E_{n})$ and $G_{E_{n}}$
are Hamiltonian.
Keywords:
unit graph, unitary Cayley graph, Eisenstein integers, Hamiltonian graph.
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Reza Jahani-Nezhad, Ali Bahrami, “Unit and unitary Cayley graphs for the ring of Eisenstein integers modulo $n$”, Ural Math. J., 7:2 (2021), 43–50
\Bibitem{JahBah21}
\by Reza~Jahani-Nezhad, Ali~Bahrami
\paper Unit and unitary Cayley graphs for the ring of Eisenstein integers modulo $n$
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 2
\pages 43--50
\mathnet{http://mi.mathnet.ru/umj148}
\crossref{https://doi.org/10.15826/umj.2021.2.003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4358912}
\elib{https://elibrary.ru/item.asp?id=47556640}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124339699}
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https://www.mathnet.ru/eng/umj148
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This publication is cited in the following 1 articles:
S. Madhumitha, Sudev Naduvath, “Graphs Defined on Rings: A Review”, Mathematics, 11:17 (2023), 3643
Citation in format AMSBIB
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