Graphs Attached to Rings Revisited

被引：38
作者：
Maimani, H. R. [4 ,5 ]
Pournaki, M. R. [3 ]
Tehranian, A. [2 ]
Yassemi, S. [1 ]
机构：
[1] Univ Tehran, Coll Sci, Sch Math Stat & Comp Sci, Tehran, Iran
[2] IAU, Sci & Res Branch, Tehran, Iran
[3] Sharif Univ Technol, Dept Math Sci, Tehran, Iran
[4] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran
[5] Shahid Rajaee Teacher Training Univ, Dept Basic Sci, Math Sect, Tehran, Iran
来源：
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING | 2011年 / 36卷 / 06期
关键词：
Chromatic index; Chromatic number; Clique number; Comaximal graph; Connectedness; Cototal graph; Counit graph; Diameter; Finite ring; Girth; Hamiltonian cycle; Hamiltonian graph; Planarity; Total graph; Unit element; Unit graph; Weakly perfect graph; Zero-divisor graph; WEAKLY PERFECT GRAPHS; COMMUTATIVE RINGS; UNIT GRAPHS; SUM; IDEMPOTENT; ELEMENTS;
D O I：
10.1007/s13369-011-0096-y
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we discuss some recent results on graphs attached to rings. In particular, we deal with comaximal graphs, unit graphs, and total graphs. We then define the notion of cototal graph and, using this graph, we characterize the rings which are additively generated by their zero divisors. Finally, we glance at graphs attached to other algebraic structures.
引用
收藏
页码：997 / 1011
页数：15
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