Reza Jahani-Nezhad     (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran, Islamic Republic of)
Ali Bahrami     (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran, Islamic Republic of)


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.


Unit graph, Unitary Cayley graph, Eisenstein integers, Hamiltonian graph

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DOI: http://dx.doi.org/10.15826/umj.2021.2.003

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