2025/10/05 by Wang, Runze
#05C57 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.05170
In a graph G, we define a set of vertices to be a strong hub set if for any two vertices in G, we can find a path between them whose internal vertices are all in this set. We define the strong hub cover pebbling number of G, denoted by hs^*(G), to be the smallest t such that for any initial configuration with t pebbles on G, we can make some pebbling moves (a pebbling move consists of removing two pebbles from a vertex v and adding one pebble to another vertex adjacent to v) so that there is a strong hub set with every vertex in it having a pebble. We determine the strong hub cover pebbling numbers of paths, stars, and books.