On the packing chromatic number of Moore graphs

Abstract The packing chromatic number χ ρ ( G ) of a graph G is the smallest integer k for which there exists a vertex coloring Γ : V ( G ) → { 1 , 2 , … , k } such that any two vertices of color i are at distance at least i + 1 . For g ∈ { 6 , 8 , 12 } , ( q + 1 , g ) -Moore graphs are ( q + 1 ) -regular graphs with girth g which are the incidence graphs of a symmetric generalized g ∕ 2 -gons of order q . In this paper we study the packing chromatic number of a ( q + 1 , g ) -Moore graph G . For g = 6 we present the exact value of χ ρ ( G ) . For g = 8 , we determine χ ρ ( G ) in terms of the intersection of certain structures in generalized quadrangles. For g = 12 , we present lower and upper bounds for this invariant when q ≥ 9 is an odd prime power.