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N, Gowri, A Kalarkop, David, Arumugam, Subramanian. (1403). On $\gamma$-free, $\gamma$-totally-free and $\gamma$-fixed sets in graphs. , 9(4), 647-654. doi: 10.22049/cco.2023.28525.1600
Gowri N; David A Kalarkop; Subramanian Arumugam. "On $\gamma$-free, $\gamma$-totally-free and $\gamma$-fixed sets in graphs". , 9, 4, 1403, 647-654. doi: 10.22049/cco.2023.28525.1600
N, Gowri, A Kalarkop, David, Arumugam, Subramanian. (1403). 'On $\gamma$-free, $\gamma$-totally-free and $\gamma$-fixed sets in graphs', , 9(4), pp. 647-654. doi: 10.22049/cco.2023.28525.1600
N, Gowri, A Kalarkop, David, Arumugam, Subramanian. On $\gamma$-free, $\gamma$-totally-free and $\gamma$-fixed sets in graphs. , 1403; 9(4): 647-654. doi: 10.22049/cco.2023.28525.1600

On $\gamma$-free, $\gamma$-totally-free and $\gamma$-fixed sets in graphs

Communications in Combinatorics and Optimization
مقاله 4، دوره 9، شماره 4، اسفند 2024، صفحه 647-654    اصل مقاله (400.95 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, India
2Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru-570 006, India
3Adjunct Professor, Department of Computer Science and Engineering, Ramco Institute of Technology, Rajapalayam-626 117, 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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