UNIT GRAPHS ASSOCIATED WITH RINGS

被引：117

作者：

Ashrafi, N. ^{[2
]}

Maimani, H. R. ^{[3
,5
]}

Pournaki, M. R. ^{[1
,5
]}

Yassemi, S. ^{[4
]}

机构：

[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran

[2] Semnan Univ, Dept Math, Semnan, Iran

[3] Shahid Rajaee Teacher Training Univ, Math Sect, Dept Basic Sci, Tehran, Iran

[4] Univ Tehran, Sch Math Stat & Comp Sci, Coll Sci, Tehran, Iran

[5] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

来源：

COMMUNICATIONS IN ALGEBRA | 2010年 / 38卷 / 08期

关键词：

Chromatic index; Connectedness; Diameter; Girth; Planarity; Unit graph; SUM;

D O I：

10.1080/00927870903095574

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this article, the basic properties of G(R) are investigated and some characterization results regarding connectedness, chromatic index, diameter, girth, and planarity of G(R) are given. (These terms are defined in Definitions and Remarks 4.1, 5.1, 5.3, 5.9, and 5.13.)

引用

页码：2851 / 2871

页数：21

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