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Co-even domination number of a modified graph by operations on a vertex or an edge | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 1، دوره 6، شماره 4، 2025، صفحه 289-295 اصل مقاله (366.83 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.22929.1204 | ||
| نویسندگان | ||
| Nima Ghanbari1؛ Saeid Alikhani* 1؛ Mohammad Ali Dehghanizadeh2 | ||
| 1Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran | ||
| 2Department of Basic Sciences, Technical and Vocational University(TVU), Tehran, Iran | ||
| چکیده | ||
| Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called co-even dominating set if the degree of vertex $v$ is even number for all $v\in V\setminus D$. The cardinality of a smallest co-even dominating set of $G$, denoted by $\gamma _{coe}(G)$, is the co-even domination number of $G$. In this paper, we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph. | ||
| کلیدواژه‌ها | ||
| Domination number؛ Co-even dominating set؛ Vertex removal؛ Edge removal؛ Contraction | ||
| مراجع | ||
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[1] S. Alikhani, On the domination polynomials of non P4-free graphs, Iran. J. Math. Sci. Inform., 8 (2013), pp. 49–55, 142.
[2] C. S. Babu and A. A. Diwan, Subdivisions of graphs: a generalization of paths and cycles, Discrete Math., 308 (2008), pp. 4479–4486.
[3] J. A. Bondy and U. S. R. Murty, Graph theory with applications, American Elsevier Publishing Co., Inc., New York, 1976.
[4] N. Ghanbari, Co-even domination number of some binary operations on graphs, Submitted. Preprint available at https://arxiv.org/abs/2111.01845.
[5] N. Ghanbari, Secure domination number of k-subdivision of graphs. Preprint available at https://arxiv.org/abs/2110.09190.
[6] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs, vol. 208 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1998.
[7] M. Makki Shaalan and A. Omran, Co-even domination in graphs, Int. J. Control Automat., 13 (2020), pp. 330–334.
[8] M. Walsh, The hub number of a graph, Int. J. Math. Comput. Sci., 1 (2006), pp. 117–124. | ||
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