2024/05/06 by Azam Sadat Ahmadi, Ahmadi, Azam Sadat, Nasrin Soltankhah +1
Computer Science · Engineering · #05C05 #05C69 #05C76 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Optimization and Packing Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2405.03237
openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set B⊆ V(G) is called a k-total limited packing set in a graph G if |B∩ N(v)|≤ k for any vertex v∈ V(G). The k-total limited packing number Lk,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 (kLPP) of graph G is a partition of V(G) into k-limited packing sets. The minimum cardinality of a kLPP is called the kLPP number of G and is denoted by χ× k(G), and we obtain some results for this parameter.