Unit graphs of rings of polynomials and power series

被引：19

作者：

Afkhami M. ^{[1
]}

Khosh-Ahang F. ^{[2
]}

机构：

[1] Department of Mathematics, University of Neyshabur, Neyshabur

[2] Department of Mathematics, Ilam University, Ilam

来源：

Arabian Journal of Mathematics | 2013年 / 2卷 / 3期

关键词：

05C75; 13A10; 13B25;

D O I：

10.1007/s40065-013-0067-0

中图分类号：

学科分类号：

摘要：

Let R be a commutative ring. The unit graph of R, denoted by G(R), is a graph with all elements of R as vertices and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ U(R) where U(R) denotes the set of all units of R. In this paper, we examine the preservation of the connectedness, diameter, girth, and some other properties, such as chromatic index, clique number and planarity of the unit graph G(R) under extensions to polynomial and power series rings. [Figure not available: see fulltext.] © 2013, The Author(s).

引用

页码：233 / 246

页数：13

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