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Independent transversal domination subdivision number of trees | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 5، دوره 11، شماره 2، شهریور 2026، صفحه 387-405 اصل مقاله (447.78 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28772.1713 | ||
| نویسندگان | ||
| P. Roushini Leely Pushpam* 1؛ K. Priya Bhanthavi2 | ||
| 1Department of Mathematics, D.B. Jain College, Chennai 600 097, Tamil Nadu, India | ||
| 2Department of Mathematics, S.D.N.B. Vaishnav College for Women, Chennai 600 044, Tamil Nadu, India | ||
| چکیده | ||
| A set $S\subseteq V $ of vertices in a graph $G=(V,E)$ is called a dominating set if every vertex in $V \setminus S $ is adjacent to a vertex in S. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. The domination subdivision number $sd_{\gamma}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the domination number. Sahul Hamid defined a dominating set which intersects every maximum independent set in $G$ to be an \textit{independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number} of $G$ and is denoted by $\gamma_{it}(G)$. We extend the idea of domination subdivision number to independent transversal domination. The independent transversal domination subdivision number of a graph $G$ denoted by $sd_{\gamma_{it}}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the independent transversal domination number. In this paper we initiate a study of this parameter with respect to trees. | ||
| کلیدواژهها | ||
| dominating set؛ Independent set؛ independent transversal dominating set؛ subdivision number | ||
| مراجع | ||
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[10] H. Wang, B. Wu, and X. An, Independent transversal domination number of a graph, arXiv preprint arXiv:1704.06093 (2017). | ||
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