آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 121 |
| تعداد مقالات | 1,448 |
| تعداد مشاهده مقاله | 1,555,853 |
| تعداد دریافت فایل اصل مقاله | 1,459,870 |
D-Distance magic labeling of $C^n_r$ | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 آذر 1404 اصل مقاله (466.97 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30451.2479 | ||
| نویسندگان | ||
| Maurice Genevieva Almeida* 1، 2؛ Tarkeshwar Singh1 | ||
| 1Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India | ||
| 2Rosary College of Commerce and Arts, Navelim, Salcete, Goa | ||
| چکیده | ||
| Let $G=(V, E)$ be a graph of order $n$. Let $D\subseteq\{0,1,2,\dots, \text{diam}(G)\}$ be nonempty. The $D$-neighborhood $N_D(x)$, of a vertex $x$ is the set of all vertices whose distance from vertex $x$ is an element in $D$, that is, $N_D(x)=\{y\in V:\ d(x,y)=m, m\in D\}$. A $D$-distance magic labeling of $G$ is a bijection $f\colon V\to \{1,2,\dots,n\}$ for which there exists a positive integer $k$, such that $\sum_{x\in N_D(v)}f(x)=k$ for all $v\in V$, where $N_D(v)$ is the $D$-open neighborhood of $v$. Let $\Gamma$ be an abelian group of order $n$. A $(\Gamma,D)$-distance magic labeling of $G$ is a bijection $l\colon V\to \Gamma$ for which there exists an element $\mu\in \Gamma$, such that $\sum_{x\in N_D(v)}l(x)=\mu$ for all $v\in V$. This paper presents the necessary and sufficient conditions for the existence of $D$-distance magic labeling for $C_n^r$ for a set $D$ containing elements in arithmetic progression. For the same set $D$, we also study the $(\Gamma, D)$-distance magic labeling of $C_n^r$ for some specific classes of abelian groups $\Gamma$. | ||
| کلیدواژهها | ||
| Distance Magic Labeling؛ Group Distance Magic Labeling؛ Circulant Graphs | ||
| مراجع | ||
|
[1] G. Chartrand, H. Jordon, V. Vatter, and P. Zhang, Graphs & Digraphs, Chapman and Hall/CRC, 2024.
[2] S. Cichacz, Distance magic $(r, t)$-hypercycles, Util. Math. 101 (2013), 283–294.
[3] S. Cichacz, Group distance magic labeling of some cycle related graphs, Australas. J. Comb. 57 (2013), 235–243.
[4] D. Froncek, Group distance magic labeling of Cartesian product of cycles., Australas. J. Comb. 55 (2013), 167–174.
[5] A. Godinho and T. Singh, Group distance magic labeling of $C_n^r$, Algorithms and Discrete Applied Mathematics (Cham) (D. Gaur and N.S. Narayanaswamy, eds.), Springer International Publishing, 2017, pp. 187–192.
[6] A. Godinho and T. Singh, Some distance magic graphs, AKCE Int. J. Graphs Comb. 15 (2018), no. 1, 1–6. https://doi.org/10.1016/j.akcej.2018.02.004
[7] A. O’Neal and P.J. Slater, An introduction to distance $D$-magic graphs, J. Indones. Math. Soc. (2011), 89–107. | ||
|
آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 28 |
||