Domination number of incidence graphs of block designs

摘要

For a 2-(v, k, λ) design D, the incidence graph of D is a bipartite graph with vertex set P∪B, the point x∈P is adjacent to the block B∈B if and only if x is contained in B. In this paper, we investigate the domination number of the incidence graphs of symmetric 2-(v, k, λ) designs and Steiner systems. Moreover, we give a sufficient condition for a design to be super-neat, and thus prove that the finite projective planes and the finite affine planes are super-neat.