Global Domination and Packing Numbers
Abbreviated Journal Title
For a graph G = (V, E), X subset of V is a global dominating set if X dominates both G and the complement graph (G) over bar. A set X C V is a packing if its pairwise members are distance at least 3 apart. The minimum number of vertices in any global dominating set is gamma(g)(G), and the maximum number in any packing is p(G). We establish relationships between these and other graphical invariants, and characterize graphs for which p(G) = p(G). Except for the two self complementary graphs on 5 vertices and when G or (G) over bar has isolated vertices, we show gamma(g)(G) <= left perpendicular n/2 right perpendicular, where n = vertical bar V vertical bar.
"Global Domination and Packing Numbers" (2011). Faculty Bibliography 2010s. 1273.