Speaker
Dr
Nancy E. Clarke
(Acadia University)
Description
For a fixed integer $k$, a set of vertices $B$ of a graph $G$ is a *$k$-limited packing* of $G$ provided that the closed neighourhood of any vertex in G contains at most $k$ elements of $B$. The size of a largest possible $k$-limited packing in $G$ is denoted $L_k(G)$ and is the $k$-limited packing number of $G$. In this talk, we investigate the 2-limited packing number of box products of paths. We show that the function \Delta[L_2(P_k \square P_n)] = L_2(P_k \square P_n) -L_2(P_k \square P_{n-1}) is eventually periodic, and thereby give closed formulas for L_2(P_k \square P_n), $k = 1, 2, \ldots, 5$. The techniques we use are suitable for establishing other types of packing and domination numbers for box products of paths and, more generally, for graphs of the form H \square P_n.
Primary author
Dr
Nancy E. Clarke
(Acadia University)
Co-author
Dr
Robert P. Gallant
(Grenfell Campus, Memorial University)
