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On independent $k$-domination number of Hamming graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 اردیبهشت 1404 اصل مقاله (368.9 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30098.2315 | ||
| نویسنده | ||
| Javad B. Ebrahimi* | ||
| Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11155-9415, Tehran, Iran | ||
| چکیده | ||
| A subset \( S \) of the vertices of a graph is called a \( k \)-dominating set if every vertex outside \( S \) has at least \( k \) neighbors in \( S \). If a \( k \)-dominating set is an independent subset of the vertices, then the set is called an independent \( k \)-dominating set. The size of the smallest such set is called the independent \( k \)-domination number of the graph. In this paper, we derive a lower bound on the independent \( k \)-domination number of Hamming graphs. For some sets of parameters, we show that this lower bound is exact. | ||
| کلیدواژه‌ها | ||
| Independent k-domination number؛ Hamming graph؛ Dominating sets؛ Graph domination؛ Covering problem | ||
| مراجع | ||
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[1] A. Blokhuis, S. Egner, H.D.L. Hollmann, and J.H. van Lint, On codes with covering radius 1 and minimum distance 2, Indag. Math. 12 (2001), no. 4, 449–452. https://doi.org/10.1016/S0019-3577(01)80033-1
[2] F. Harary and M. Livingston, Independent domination in hypercubes, Appl. Math. Lett. 6 (1993), no. 3, 27–28. https://doi.org/10.1016/0893-9659(93)90027-K
[3] T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, Domination in Graphs: Core Concepts, Springer International Publishing, 2023.
[4] Z.L. Nagy, On the number of k-dominating independent sets, J. Graph Theory 84 (2017), no. 4, 566–580. https://doi.org/10.1002/jgt.22042
[5] A. Włoch, On 2-dominating kernels in graphs, Australas. J. Combin. 53 (2012), 273–284. | ||
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