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On $\gamma$-free, $\gamma$-totally-free and $\gamma$-fixed sets in graphs | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 خرداد 1402 اصل مقاله (399.35 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2023.28525.1600 | ||
نویسندگان | ||
Gowri N1؛ David A Kalarkop2؛ Subramanian Arumugam* 3 | ||
1Department of Mathematics, S. D. College, Alappuzha-690 104 | ||
2DOS in Mathematics Manasagangotri | ||
3Director (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626 126 Tamil Nadu, India | ||
چکیده | ||
Let $G=(V,E)$ be a connected graph. A subset $S$ of $V$ is called a $\gamma$-free set if there exists a $\gamma$-set $D$ of $G$ such that $S \cap D= \emptyset$. If further the induced subgraph $H=G[V-S]$ is connected, then $S$ is called a $cc$-$\gamma$-free set of $G$. We use this concept to identify connected induced subgraphs $H$ of a given graph $G$ such that $\gamma(H) \leq \gamma(G)$. We also introduce the concept of $\gamma$-totally-free and $\gamma$-fixed sets and present several basic results on the corresponding parameters. | ||
کلیدواژهها | ||
Domination؛ domination number؛ $gamma$-set؛ $gamma$-free set؛ $gamma$-totally-free set | ||
مراجع | ||
[1] G. Chartrand, L. Lesniak, and P. Zhang, Graphs & digraphs, CRC, Boca Raton, 2016.
[2] T.W. Haynes, S.T. Hedetniemi, and P.J. Salter, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
[3] S.M. Hedetniemi, S.T. Hedetniemi, and R. Reynolds, Combinatorial problems on chessboards: II, Domination in Graphs, Advanced Topics (T.W. Haynes, S.T. Hedetniemi, and P.J. Salter, eds.), Marcel Dekker, Inc., New York, 1998, pp. 133– 192. [4] N. Jafari Rad, D.A. Mojdeh, R. Musawi, and E. Nazari, Total domination in cubic knödel graphs, Commun. Comb. Optim. 6 (2021), no. 2, 221–230.
[5] E. Sampathkumar and P.S. Neeralagi, Domination and neighbourhood critical, fixed, free and totally free points, Indian J. Statistics (1992), 403–407. | ||
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