Zobrazeno 1 - 10
of 2 252
pro vyhledávání: '"zero-divisor graphs"'
Autor:
Kumar, Ravindra, Prakash, Om
For a graph $G= (V, E)$, a Roman dominating function is a map $f : V \rightarrow \{0, 1, 2\}$ satisfies the property that if $f(v) = 0$, then $v$ must have adjacent to at least one vertex $u$ such that $f(u)= 2$. The weight of a Roman dominating func
Externí odkaz:
http://arxiv.org/abs/2412.07510
Autor:
Dung, Le Xuan, Vu, Thanh
We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We then classify all positive integer $n$ such that the zero divisor grap
Externí odkaz:
http://arxiv.org/abs/2411.05251
In this work, we study the eccentricity spectra of zero divisor graphs (ZDGs) associated with the ring $\mathbb{Z}_n.$ While previous studies have examined the Laplacian and distance Laplacian spectra of ZDGs, the eccentricity spectra have remained l
Externí odkaz:
http://arxiv.org/abs/2409.13186
In this paper, we prove that for all $m\geq 1$ and $n=1$, the graph $ m\Gamma(\mathbb{Z}_9)+n\Gamma(\mathbb{Z}_4)$, for all $n\geq 1$, and $m=1$, the graph $m\overline{\Gamma(\mathbb{Z}_6)}+n\Gamma(\mathbb{Z}_9)$, for all $m\geq1$, $[m\Gamma(\mathbb{
Externí odkaz:
http://arxiv.org/abs/2407.08211
This paper explores the concept of multiset dimensions (Mdim) of compressed zero-divisor graphs (CZDG) associated with rings. The authors investigate the interplay between the ring-theoretic properties of a ring $R$ and the associated compressed zero
Externí odkaz:
http://arxiv.org/abs/2405.06187
The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay between t
Externí odkaz:
http://arxiv.org/abs/2405.04934
This article investigates multiset dimensions in zero divisor graphs (ZD-graphs) associated with rings. Through rigorous analysis, we establish general bounds for the multiset dimension (Mdim) in ZD-graphs, exploring various commutative rings includi
Externí odkaz:
http://arxiv.org/abs/2405.06180
Autor:
Alikhani, Saeid, Aghaei, Fatemeh
The domination polynomial (the total domination polynomial) of a graph $ G $ of order $ n $ is the generating function of the number of dominating sets (total dominating sets) of $ G $ of any size. In this paper, we study the domination polynomial an
Externí odkaz:
http://arxiv.org/abs/2404.13539
Autor:
Fareeha Jamal, Muhammad Imran
Publikováno v:
AIMS Mathematics, Vol 9, Iss 9, Pp 23979-23996 (2024)
In the present article, we give the distance spectrum of the zero divisor graphs of the commutative rings $ \mathbb{Z}_{t}[x]/\langle x^{4} \rangle $ ($ t $ is any prime), $ \mathbb{Z}_{t^2}[x] / \langle x^2 \rangle $ ($ t \geq 3 $ is any prime) and
Externí odkaz:
https://doaj.org/article/56c445e83786469eab43149b5fc88fed
Autor:
Rather, Bilal Ahmad
For a commutative ring $R,$ with non-zero zero divisors $Z^{\ast}(R)$. The zero divisor graph $\Gamma(R)$ is a simple graph with vertex set $Z^{\ast}(R)$, and two distinct vertices $x,y\in V(\Gamma(R))$ are adjacent if and only if $x\cdot y=0.$ In th
Externí odkaz:
http://arxiv.org/abs/2401.02554