کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902814 | 1632247 | 2016 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Distances in zero-divisor and total graphs from commutative rings-A survey
ترجمه فارسی عنوان
فاصله در تقسیم صفر و نمودار کل از حلقه های تعاملی - یک نظرسنجی
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کلمات کلیدی
حلقه متناوب، نمودار صفر تقسیم، نمودار مجموع، تسلط،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings. For a commutative ring R with non-zero identity, we denote the set of zero-divisors and unit elements of R by Z(R) and U(R), respectively. One of the associated graphs to a ring R is the zero-divisor graph; it is a simple graph with vertex set Z(R)â{0}, and two vertices x and y are adjacent if and only if xy=0. This graph was first introduced by Beck, where all the elements of R are considered as the vertices. Anderson and Badawi, introduced the total graph of R, as the simple graph with all elements of R as vertices, and two distinct vertices x and y are adjacent if and only if x+yâZ(R). For a given graph G, the concept of connectedness, diameter and girth are always of great interest. Several authors extensively studied about the zero-divisor and total graphs from commutative rings. In this paper, we present a survey of results obtained with regard to distances in zero-divisor and total graphs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: AKCE International Journal of Graphs and Combinatorics - Volume 13, Issue 3, December 2016, Pages 290-298
Journal: AKCE International Journal of Graphs and Combinatorics - Volume 13, Issue 3, December 2016, Pages 290-298
نویسندگان
T. Tamizh Chelvam, T. Asir,