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Further results on the j-independence number of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 9، شماره 1، خرداد 2024، صفحه 1-11 اصل مقاله (398.91 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.28012.1417 | ||
| نویسندگان | ||
| Ahmed Bouchou1؛ Mustapha Chellali* 2 | ||
| 1LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria | ||
| 2LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria | ||
| چکیده | ||
| In a graph $G$ of minimum degree $\delta$ and maximum degree $\Delta$, a subset $S$ of vertices of $G$ is $j$-independent, for some positive integer $j,$ if every vertex in $S$ has at most $j-1$ neighbors in $S$. The $j$-independence number $\beta_{j}(G)$ is the maximum cardinality of a $j$-independent set of $G$. We first establish an inequality between $\beta_{j}(G)$ and $\beta_{\Delta}(G)$ for $1\leq j\leq\delta-1$. Then we characterize all graphs $G$ with $\beta_{j}(G)=\beta_{\Delta}(G)$ for $j\in\{1,\dots,\Delta-1\}$, where the particular cases $j=1,2,\delta-1$ and $\delta$ are well distinguished. | ||
| کلیدواژه‌ها | ||
| j-independent sets؛ j-domination number؛ j-dominating sets | ||
| مراجع | ||
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[5] A. Hansberg, B. Randerath, and . Volkmann, Claw-free graphs with equal 2-domination and domination numbers, Filomat 30 (2016), no. 10, 2795–2801.
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[7] B. Reed, Paths, stars and the number three, Comb. Prob. Comp 5 (1996), no. 3, 277–295. https://doi.org/10.1017/S0963548300002042 | ||
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