دانشگاه گیلان
معاونت پژوهش و فناوری دانشگاه گیلان
انتشارات دانشگاه گیلان

 آمار

تعداد نشریات31
تعداد شماره‌ها757
تعداد مقالات7,162
تعداد مشاهده مقاله10,347,626
تعداد دریافت فایل اصل مقاله6,937,292
Nazim, M., Abdioglu, C., Rehman, N., Mir, Sh. A.. (1403). On the genus and crosscap of the total graph of commutative rings with respect to multiplication. فیزیولوژی و بیوتکنولوژی آبزیان, (), -. doi: 10.22124/jart.2024.27463.1667
M. Nazim; C. Abdioglu; N. Rehman; Sh. A. Mir. "On the genus and crosscap of the total graph of commutative rings with respect to multiplication". فیزیولوژی و بیوتکنولوژی آبزیان, , , 1403, -. doi: 10.22124/jart.2024.27463.1667
Nazim, M., Abdioglu, C., Rehman, N., Mir, Sh. A.. (1403). 'On the genus and crosscap of the total graph of commutative rings with respect to multiplication', فیزیولوژی و بیوتکنولوژی آبزیان, (), pp. -. doi: 10.22124/jart.2024.27463.1667
Nazim, M., Abdioglu, C., Rehman, N., Mir, Sh. A.. On the genus and crosscap of the total graph of commutative rings with respect to multiplication. فیزیولوژی و بیوتکنولوژی آبزیان, 1403; (): -. doi: 10.22124/jart.2024.27463.1667

On the genus and crosscap of the total graph of commutative rings with respect to multiplication

Journal of Algebra and Related Topics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1403
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2024.27463.1667
نویسندگان
M. Nazim* 1؛ C. Abdioglu2؛ N. Rehman3؛ Sh. A. Mir4
1School of Computational Sciences, Faculty of Science and Technology, JSPM University, Pune-412207, India
2Department of Mathematics Faculty of Education Karamanoglu Mehmetbey University Karaman - Turkey
3Department of Mathematics Aligarh Muslim University Aligarh
4Department of Mathematics, Aligarh Muslim University, Aligarh
چکیده
Let $\mathcal{S}$ be a commutative ring and $Z(\mathcal{S})$ be its zero-divisors set.
The total graph of $\mathcal{S}$ with respect to multiplication, denoted by $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}))$, is an undirected graph with vertex set as the ring elements $\mathcal{S}$ and two distinct vertices $\alpha$ and $\beta$ are adjacent if and only if $\alpha\beta \in Z(\mathcal{S})$.
The graph $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ is a subgraph of $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}))$ with vertex set $\mathcal{S}^*$ (set of nonzero elements of $\mathcal{S}$).
In this paper, we characterize finite rings $\mathcal{S}$ for which $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ belongs to some well-known families of graphs. Further, we classify the finite rings $\mathcal{S}$ for which $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ is planar, toroidal or double toroidal. Finally, we analyze the finite rings $\mathcal{S}$ for which the graph $T_{Z(\mathcal{S})}(\Gamma(\mathcal{S}^*))$ has crosscap at most two.
کلیدواژه‌ها
Crosscap of a graph؛ genus of a graph؛ total graph with respect to multiplication؛ zero-divisor graph
آمار
تعداد مشاهده مقاله: 81


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب