آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 122 |
| تعداد مقالات | 1,538 |
| تعداد مشاهده مقاله | 1,628,301 |
| تعداد دریافت فایل اصل مقاله | 1,525,832 |
Revisiting the outer-weakly convex domination number in graph products | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 اردیبهشت 1405 اصل مقاله (554.43 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30308.2408 | ||
| نویسندگان | ||
| Bijo S. Anand1؛ Ullas chandran S V* 2؛ Jonecis A. Dayap3؛ Leomarich F. Casinillo4؛ Karen Luz P. Yap4 | ||
| 1Department of Mathematics, Sree Narayana College, Punalur - 691305, Kollam, Kerala, India | ||
| 2Department of Mathematics, Mahatma Gandhi College, Thiruvananthapuram - 695004, Kerala, India | ||
| 3University of San Jose - Recoletos, Philippines | ||
| 4Visayas State University, Philippines | ||
| چکیده | ||
| Let $G = (V, E)$ be a simple undirected connected graph. A set $C \subseteq V(G)$ is weakly convex in $G$ if for every two vertices $u,v$ in $G$, there exists a $u-v$ geodesic whose vertices are in $C$. A set $C \subseteq V$ is an outer-weakly convex dominating set if every vertex not in $C$ is adjacent to some vertex in $C$ and the set $V(G)\setminus C$ is weakly convex in $G$. The outer-weakly convex domination number of graph $G$, denoted by $\widetilde{ \gamma}_{wcon}(G)$, is the minimum cardinality of an outer-weakly convex dominating set of graph $G$. In this paper, we determine the outer-weakly convex domination number of two graphs under the Cartesian, strong and lexicographic products, and discuss some important combinatorial findings. | ||
| کلیدواژهها | ||
| convex set؛ dominating set؛ weakly-convex set | ||
| مراجع | ||
|
[1] R. Araújo and R. Sampaio, Domination and convexity problems in the target set selection model, Discrete Appl. Math. 330 (2023), 14–23. https://doi.org/10.1016/j.dam.2022.12.021
[2] J. C´aceres, C. Hernando, M. Mora, I.M. Pelayo, M.L. Puertas, C. Seara, and D.R. Wood, On the metric dimension of cartesian products of graphs, SIAM J. Discrete Math. 21 (2007), no. 2, 423–441. https://doi.org/10.1137/050641867
[3] L.F. Casinillo, A note on Fibonacci and Lucas number of domination in path, Electron. J. Graph Theory Appl. 6 (2018), no. 2, 317–325. https://dx.doi.org/10.5614/ejgta.2018.6.2.11
[4] L.F. Casinillo, New counting formula for dominating sets in path and cycle graphs, J. Fund. Math. Appl. 3 (2020), no. 2, 170–177. https://doi.org/10.14710/jfma.v3i2.9325
[5] G. Chartrand and P. Zhang, A First Course in Graph Theory, Courier Corporation, 2013.
[6] E.J. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), no. 3, 247–261. https://doi.org/10.1002/net.3230070305 [7] J.A. Dayap, R. Alcantara, and R. Anoos, Outer-weakly convex domination number of graphs, Commun. Comb. Optim. 5 (2020), no. 2, 207–215. https://doi.org/10.22049/cco.2020.26871.1154
[8] J.A. Dayap and E.L. Enriquez, Outer-convex domination in the composition and cartesian product of graphs, Journal of Global Research in Mathematical Archives 6 (2019), no. 3, 34–42.
[9] J.A. Dayap and E.L. Enriquez, Outer-convex domination in graphs, Discrete Math. Algorithms Appl. 12 (2020), no. 1, 2050008. https://doi.org/10.1142/S1793830920500081
[10] F. Harary and J. Nieminen, Convexity in graphs, Journal of Differential Geometry 16 (1981), no. 2, 185–190.
[11] T.W. Haynes, S.T. Hedetniemi, and P. Slater, Domination in Graphs: Advanced Topics, Routledge, 1998.
[12] M.A. Henning and A. Yeo, Total Domination in Graphs, vol. 1, Springer, 2013.
[13] M. Jannesari and B. Omoomi, The metric dimension of the lexicographic product of graphs, Discrete Math. 312 (2012), no. 22, 3349–3356. https://doi.org/10.1016/j.disc.2012.07.025
[14] I.M. Pelayo, Geodesic Convexity in Graphs, vol. 577, Springer, 2013.
[15] M. Tavakoli, F. Rahbarnia, and A.R. Ashrafi, Note on strong product of graphs, Kragujevac J. Math. 37 (2013), no. 1, 187–193. | ||
|
آمار تعداد مشاهده مقاله: 118 تعداد دریافت فایل اصل مقاله: 25 |
||