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One of the purposes of this paper is to clarify the strong analogy between potential theory on the open unit disk and the homogeneous tree, to which we dedicate an introductory section. We then exemplify this analogy by a study of Riesz measures. Starting from interesting work by Favorov and Golinskii [10], we consider subharmonic functions on the open unit disk, resp. on the homogenous tree. Supposing that we can control the way how those functions may tend to infinity at the boundary, we derive moment type conditions for the Riesz measures. One one hand, we generalise the previous results of [10] for the disk, and on the other hand, we show how to obtain analogous results in the discrete setting of the tree.

We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one unlooped vertex. We also prove that this factorization can be computed in O(m) time, where m is the number of edges of the given graph.

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В статті представлений біоморфологічний аналіз ліхенобіоти Єланецько-Інгульського регіону. Всього для дослідженої ліхенобіоти виділено 19 біоморф.