energy and wiener index of zero-divisor graphs
نویسندگان
چکیده
let r be a commutative ring and (r) be its zerodivisor graph. in this article, we studywiener index and energy of γ(zn ) where n = pq or n = p2q and p, q are primes. a matlabcode for our calculations is also presented.
منابع مشابه
On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...
متن کاملA generalization of zero-divisor graphs
In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores
متن کامل$C_4$-free zero-divisor graphs
In this paper we give a characterization for all commutative rings with $1$ whose zero-divisor graphs are $C_4$-free.
متن کاملon zero-divisor graphs of quotient rings and complemented zero-divisor graphs
for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...
متن کاملEnergy and Wiener Index of Unit Graphs
In this paper, we are giving MATLAB program to find the energy and Wiener index of unit graphs. Our program demonstrates an intrinsic relationship between the elements of ring and structural properties of graphs. The unit graph G(Zn) turns out to be strongly regular when n = 2k. Several new directions for further research are also indicated by means of raising problems.
متن کاملZero Divisor Graphs of Posets
In 1988, Beck [10] introduced the notion of coloring of a commutative ring R. Let G be a simple graph whose vertices are the elements of R and two vertices x and y are adjacent if xy = 0. The graph G is known as the zero divisor graph of R. He conjectured that, the chromatic number χ(G) of G is same as the clique number ω(G) of G. In 1993, Anderson and Naseer [1] gave an example of a commutativ...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
iranian journal of mathematical chemistryناشر: university of kashan
ISSN 2228-6489
دوره 2
شماره Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday) 2011
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023