A graph is k-domination-critical if gamma(G) = k, and for any edge e not in G, gamma(G + e) = k - 1. In this paper we show that the diameter of a domination k-critical graph with k greater-than-or-equal-to 2 is at most 2k - 2. We also show that for every k greater-than-or-equal-to 2, there is a k-domination-critical graph having diameter [(3/2)k - 1]. We also show that the diameter of a 4-domination-critical graph is at most 5. (C) 1994 John Wiley & Sons, Inc.

In this paper we investigate some of the properties of harmonic and subharmonic functions defined on n-connected domain G. In particular, we study the behavior of subharmonic functions at every point of the boundary of G. We prove that if f is subharmonic and uf is the least harmonic majorant of f then the lim sup taken along the normal to the boundary of G of f(z)P(z, x) converges to the singular part of the boundary measure of uf evaluated at x. The result is true for every x belonging to the boundary of G.