整数模Eisensete环的单位和单位CAYLEY图

Q3 Mathematics

Ural Mathematical Journal Pub Date : 2021-12-30 DOI:10.15826/umj.2021.2.003

R. Jahani-Nezhad, Ali Bahrami

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引用次数: 0

摘要

设\({E}_{n}\)为以\(n\)为模的爱森斯坦整数环。我们分别用\(G({E}_{n})\)和\(G_{{E}_{n}}\)表示\({E}_{n}\)的单位图和酉Cayley图。本文给出了这些图的直径、周长、团数和色数的取值。我们还证明了对于每个\(n>1\)，图\(G(E_{n})\)和\(G_{E_{n}}\)是哈密顿的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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UNIT AND UNITARY CAYLEY GRAPHS FOR THE RING OF EISENSTEIN INTEGERS MODULO \(n\)

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.

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来源期刊

Ural Mathematical Journal Mathematics-Mathematics (all)

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks