A KIND OF GRAPH STRUCTURE ASSOCIATED WITH ZERO-DIVISORS OF MONOID RINGS
عنوان مقاله: A KIND OF GRAPH STRUCTURE ASSOCIATED WITH ZERO-DIVISORS OF MONOID RINGS
شناسه ملی مقاله: JR_JAS-11-2_004
منتشر شده در در سال 1403
شناسه ملی مقاله: JR_JAS-11-2_004
منتشر شده در در سال 1403
مشخصات نویسندگان مقاله:
Mohammad Etezadi - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Abdollah Alhevaz - Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box ۳۱۶-۳۶۱۹۹۹۵۱۶۱, Shahrood, Iran
خلاصه مقاله:
Mohammad Etezadi - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Abdollah Alhevaz - Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box ۳۱۶-۳۶۱۹۹۹۵۱۶۱, Shahrood, Iran
Let R be an associative ring and M be a monoid. In this paper, we introduce new kind of graph structure asociated with zero-divisors of monoid ring R[M], calling it the M-Armendariz graph of a ring R and denoted by A(R,M). It is an undirected graph whose vertices are all non-zero zero-divisors of the monoid ring R[M] and two distinct vertices \alpha=a_{۱}g_{۱}+\cdots+ a_{n}g_{n} and \beta=b_{۱}h_{۱}+\cdots+b_{m}h_{m} are adjacent if and only if a_{i}b_{j}=۰ or b_{j}a_{i}=۰ for all i,j. We investigate some graph properties of A(R,M) such as diameter, girth, domination number and planarity. Also, we get some relations between diameters of the M-Armendariz graph A(R,M) and that of zero divisor graph \Gamma(R[M]), where R is a reversible ring and M is a unique product monoid.
کلمات کلیدی: M-Armendariz graph, diameter, unique product monoid, monoid ring, domination number
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1686621/