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On $k$-(total) limited packing in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 بهمن 1403 اصل مقاله (457.15 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29709.2125 | ||
| نویسندگان | ||
| Azam Sadat Ahmadi1؛ Nasrin Soltankhah* 2 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| چکیده | ||
| A set $B\subseteq V(G)$ is called a $k$-total limited packing set in a graph $G$ if $|B\cap N(v)|\leq k$ for any vertex $v\in V(G)$. The $k$-total limited packing number $L_{k,t}(G)$ is the maximum cardinality of a $k$-total limited packing set in $G$. Here, we give some results on the $k$-total limited packing number of graphs emphasizing trees, especially when $k=2$. We also study the $2$-(total) limited packing number of some product graphs. A $k$-limited packing partition ($k$LPP) of graph $G$ is a partition of $V(G)$ into $k$-limited packing sets. The minimum cardinality of a $k$LPP is called the $k$LPP number of $G$ and is denoted by $\chi_{\times k}(G)$, and we obtain some results for this parameter. | ||
| کلیدواژه‌ها | ||
| limited packing؛ $k$-limited packing partition number؛ graph products | ||
| مراجع | ||
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