For an ordered k-decomposition D = {G1, G2, . . . , Gk} of a connected graph G and an edge e of G, the D-code of e is the k-tuple cD(e) = (d(e, G1), d(e, G2), . . . , d(e, Gk)), where d(e, Gi) is the distance from e to Gi . A decomposition D is resolving if every two distinct edges of G have distinct D-codes. The minimum k for which G has a resolving k-decomposition is its decomposition dimension dimd(G). A resolving decomposition D of G is connected if each Gi is connected for 1 ≤ i ≤ k. The minimum k for which G has a connected resolving k-decomposition is its connected decomposition number cd(G). Thus 2 ≤ dimd(G) ≤ cd(G) ≤ m for every connected graph G of size m ≥ 2. All nontrivial connected graphs with connected decomposition number 2 or m are characterized. We provide bounds for the connected decomposition number of a connected graph in terms of its size, diameter, girth, and other parameters. A formula for the connected decomposition number of a nonpath tree is established. It is shown that, for every pair a, b of integers with 3 ≤ a ≤ b, there exists a connected graph G with dimd(G) = a and cd(G) = b.
During the vegetation period from June to October 1990 the growth, photosynthetic C02-fixation, pigment content and chlorophyll (Chl) fluorescence characteristics were compared in the needles of 5-year-old spruce dones Picea abies (L.) Karst., cultivated for two years on the soil and the sand, with or without addition of minerál fertilizers. Minerál deflciency in the spruce dones grown on the sand instead of a humus containing soil resulted in somewhat reduced lengthwise growth of shoots and needles, lower level of Chl and carotenoids (Car), as well as lower net photosynthetic rates (F^) per needle area unit and in generál also lower stomata conductance (gH2o) values. In contrast, the variable Chl fluorescence measured via the Chl fluorescence decrease ratio (Rfj = fd/fs) was only little affected, indicating an intemal íunctional photosynthetic apparatus even under minerál deflciency with a lower Chl content. In fact, Fj,} expressed on Chl basis was even signiflcantly higher in the newly developed 1990 needles of the sand cultures than in the soil ones. Application of a forestry fertilizer with basic minerals (K, Ca, Mg and some N) to the sand cultures increased growth of shoots and needles, levels of Chl and Čar, F^ and stomata conductance, and decreased the Chl fluorescence ratio F690/F735 and lability of the photosynthetic apparatus, as also seen in increased values of the ratio Chl/Car (a+b/x+c). The hasič minerál elements are thus necessaiy for the photosynthetic apparatus development, as well as stability of its pigment content and physiological function.