جستجوی مقالات مرتبط با کلیدواژه « genus » در نشریات گروه « ریاضی »

Let $(L,\wedge,\vee)$ be a lattice with a least element $0$. The annihilating-ideal graph of $L$, denoted by $\mathbb{AG}(L)$, is a graph whose vertex-set is the set of all non-trivial ideals of $L$ and, for every two distinct vertices $I$ and $J$, the vertex $I$ is adjacent to $J$ if and only if $I\wedge J=\{0\}$. In this paper, we characterize all lattices $L$ whose the graph $\mathfrak{L}(\mathbb{AG}(L))$ is toroidal.

For a non-abelian group $G$, its commuting conjugacy class graph $mathcal{CCC}(G)$ is a simple undirected graph whose vertex set is the set of conjugacy classes of the non-central elements of $G$ and two distinct vertices $x^G$ and $y^G$ are adjacent if there exists some elements $x' in x^G$ and $y' in y^G$ such that $x'y' = y'x'$. In this paper we compute the genus of $mathcal{CCC}(G)$ for six well-known classes of non-abelian two-generated groups (viz. $D_{2n}, SD_{8n}, Q_{4m}, V_{8n}, U_{(n, m)}$ and $G(p, m, n)$) and determine whether $mathcal{CCC}(G)$ for these groups are planar, toroidal, double-toroidal or triple-toroidal.

Let R be a non-domain commutative ring with identity and A∗(R) be the set of non-zero ideals with non-zero annihilators. We call an ideal I1 of R, an annihilating-ideal if there exists a non-zero ideal I2 of R such that I1I2 = (0). The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) and two distinct vertices I1 and I2 are adjacent if and only if I1I2 = (0). In this paper, we characterize all commutative Artinian non-local rings R for which AG(R) has genus one.