Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Classification of posets using zero-divisor graphs

In: Mathematica Slovaca, vol. 68, no. 1
Maryam Tavakkoli - Arsham Borumand Saeid - Nosratollah Shajareh Poursalavati
Detaily:
Rok, strany: 2018, 21 - 32
Kľúčové slová:
partially ordered set, zero-divisor graph, reduced graph, serried graph
O článku:
Halaš and Jukl associated the zero-divisor graph $G$ to a poset $(X,\leq)$ with zero by declaring two distinct elements $x$ and $y$ of $X$ to be adjacent if and only if there is no non-zero lower bound for $\set{x,y}$. We characterize all the graphs that can be realized as the zero-divisor graph of a poset. Using this, we classify posets whose zero-divisor graphs are the same. In particular we show that if $V$ is an $n$-element set, then there exist $\sum_{\log_2(n+1)\leq k\leq n}^{}\binom{n}{k}\binom{2^k-k-1}{n-k}$ reduced zero-divisor graphs whose vertex sets are $V$.
Ako citovať:
ISO 690:
Tavakkoli, M., Saeid, A., Poursalavati, N. 2018. Classification of posets using zero-divisor graphs. In Mathematica Slovaca, vol. 68, no.1, pp. 21-32. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0076

APA:
Tavakkoli, M., Saeid, A., Poursalavati, N. (2018). Classification of posets using zero-divisor graphs. Mathematica Slovaca, 68(1), 21-32. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0076
O vydaní:
Publikované: 23. 2. 2018