آمار
| تعداد نشریات | 5 |
| تعداد شمارهها | 116 |
| تعداد مقالات | 1,347 |
| تعداد مشاهده مقاله | 1,352,430 |
| تعداد دریافت فایل اصل مقاله | 1,293,528 |
On the zero forcing number of complementary prism graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 10، شماره 3، آذر 2025، صفحه 519-530 اصل مقاله (422.51 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27819.1362 | ||
| نویسندگان | ||
| M.R. Raksha1، 2؛ Charles Dominic* 1 | ||
| 1Department of Mathematics, CHRIST (Deemed to be university), Bengaluru-560029, Karnataka, India | ||
| 2Department of Mathematics, RV College of Engineering, Bengaluru-560059, Karnataka, India | ||
| چکیده | ||
| The zero forcing number of a graph is the minimum cardinality among all the zero forcing sets of a graph $G$. The aim of this article is to compute the zero forcing number of complementary prism graphs. Some bounds on the zero forcing number of complementary prism graphs are presented. The remainder of this article discusses the following result. Let $G$ and $\overline{G }$ be connected graphs. Then $Z(G\overline{G})\leq n-1$ if and only if there exists two vertices $v_i,v_j \in V(G)$ and $i\neq j$ such that, either $N(v_i) \subseteq N(v_j)$ or $N[v_i] \subseteq N[v_j]$ in $G$. | ||
| کلیدواژهها | ||
| zero forcing set؛ zero forcing number؛ complementary prism graph | ||
| مراجع | ||
|
[1] D. Burgarth, S. Bose, C. Bruder, and V. Giovannetti, Local controllability ofquantum networks, Physical Review A 79 (2009), no. 6, Article ID: 060305. https://doi.org/10.1103/PhysRevA.79.060305
[2] D. Burgarth and V. Giovannetti, Full control by locally induced relaxation, Physical Review Lett. 99 (2007), no. 10, Article ID: 100501. https://doi.org/10.1103/PhysRevLett.99.100501
[3] D. Burgarth, V. Giovannetti, L. Hogben, S. Severini, and M. Young, Logic circuits from zero forcing, Natural computing 14 (2015), no. 3, 485–490. https://doi.org/10.1007/s11047-014-9438-5
[4] S. Butler and M. Young, Throttling zero forcing propagation speed on graphs, Australas. J. Combin. 57 (2013), 65–71.
[5] B. Chaluvaraju and V. Chaitra, Roman domination in complementary prism graphs, Math. Combin. 2 (2012), 24–31.
[6] L. Eroh, C.X. Kang, and E. Yi, On zero forcing number of graphs and their complements, Discrete Math. Algorithms Appl. 7 (2015), no. 1, Article ID: 1550002. https://doi.org/10.1142/S1793830915500020
[7] M. Gentner, L.D. Penso, D. Rautenbach, and U.S. Souza, Extremal values and bounds for the zero forcing number, Discrete Appl. Math. 214 (2016), 196–200. https://doi.org/10.1016/j.dam.2016.06.004
[8] M. Gentner and D. Rautenbach, Some bounds on the zero forcing number of a graph, Discrete Appl. Math. 236 (2018), 203–213. https://doi.org/10.1016/j.dam.2017.11.015
[9] AIM Minimum Rank-Special Graphs Work Group Work, Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl. 428 (2008), no. 7, 1628–1648. https://doi.org/10.1016/j.laa.2007.10.009
[10] T.W. Haynes, M.A. Henning, P.J. Slater, and L.C. van der Merwe, The complementary product of two graphs, Bull. Ins. Combin. Appl. 51 (2007), 21–30.
[11] T. Kalinowski, N. Kamčev, and B. Sudakov, The zero forcing number of graphs, SIAM J. Discrete Math. 33 (2019), no. 1, 95–115. https://doi.org/10.1137/17M1133051
[12] L. Lu, B. Wu, and Z. Tang, Proof of a conjecture on the zero forcing number of a graph, Discrete Appl. Math. 213 (2016), 233–237. https://doi.org/10.1016/j.dam.2016.05.009
[13] Z. Montazeri and N. Soltankhah, Zero forcing number for Cartesian product of some graphs, Commun. Comb. Optim., 9 (2024), no. 4, 635–646. https://doi.org/10.22049/cco.2023.28177.1471
[14] D.B. West, Introduction to graph theory, vol. 2, Prentice hall Upper Saddle River, 2001. | ||
|
آمار تعداد مشاهده مقاله: 456 تعداد دریافت فایل اصل مقاله: 1,652 |
||