Graham's pebbling conjecture on the product of generalized friendship graphs
Wen-Ya Li · 2008
The pebbling number of a connected graph G is the smallest number f(G) such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified but arbitrary vertex by a sequence of pebbling moves.Graham conjectured that for any connected graphs G and H,f(G×H)≤f(G)f(H).In this paper,Graham's conjecture when H is a friendship graph or a generalized friendship graph and G is a graph with the two-pebbling property is proved.As a corollary, Graham's conjecture holds when G and H are friendship graphs or generalized friendship graphs.