Geodesic
Unit and unitary Cayley graphs for the ring of Eisenstein integers modulo $n$
Ural mathematical journal, Tome 7 (2021) no. 2, pp. 43-50

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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. 
@article{UMJ_2021_7_2_a2,
     author = {Reza Jahani-Nezhad and Ali Bahrami},
     title = {Unit and unitary {Cayley} graphs for the ring of {Eisenstein} integers modulo $n$},
     journal = {Ural mathematical journal},
     pages = {43--50},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a2/}
}
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Reza Jahani-Nezhad; Ali Bahrami. Unit and unitary Cayley graphs for the ring of Eisenstein integers modulo $n$. Ural mathematical journal, Tome 7 (2021) no. 2, pp. 43-50. http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a2/