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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Journal of Algebra and Related Topics
- نوع مقاله: Journal Article
- کلمات کلیدی: Prime submodule,Annihilator submodule,Intersection graph
- چکیده:
- چکیده انگلیسی: Let $R$ be a commutative ring and $M$ be an $R$-module. The intersection graph of annihilator
submodules of $M$, denoted by ${GA(M)}$, is a simple undirected graph whose vertices are the
classes of elements of $Z(M)setminus {rm Ann}_R(M)$ and two distinct classes $[a]$ and
$[b]$ are adjacent if and only if ${rm Ann}_M(a)cap {rm Ann}_M(b)not=0$. In this paper, we study
the diameter and girth of $overline{GA(M)}$. Furthermore, we calculate the domination number,
metric dimension, adjacency metric dimension and local metric dimension of $overline{GA(M)}$.- انتشار مقاله: 03-12-1398
- نویسندگان: Sh. Payrovi,S. B. Pejman,S. Babaei
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Finite group,Connected graph,star graph
- چکیده:
- چکیده انگلیسی: Let $G$ be a group. The order graph of $G$ is the (undirected)
graph $Gamma(G)$,
those whose vertices are non-trivial subgroups of $G$ and two distinct
vertices $H$ and $K$ are adjacent if and only if either
$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate the
interplay between the group-theoretic properties of $G$ and the
graph-theoretic properties of $Gamma(G)$. For a finite group
$G$, we show that $Gamma(G)$ is a connected graph with diameter at most
two, and $Gamma(G)$ is a complete graph if
and only if $G$ is a $p$-group for some prime number $p$. Furthermore,
it is shown that $Gamma(G)=K_5$ if and only if either
$Gcong C_{p^5}, C_3times C_3$, $C_2times
C_4$ or $Gcong Q_8$.- انتشار مقاله: 31-01-1393
- نویسندگان: SH. Payrovi,H. Pasebani
- مشاهده