Abstract
A simple but general dissimilarity characteristic theorem was used in [i] to derive gerLerating functions for counting various classes of graphs. We propose to use this result in a slightly generalized form, stated below as Theorem, to give new and short derivations of Otter's dissimilarity theorem [7], its generalization to cacti [3] (formerly called Husimi trees), and an elementary theorem for graphs [2]. In general we follow standard terminology on graphs (K6nig [6]); our graphs are finite, nonempty, and may have isolated points. A block of a graph (Glied in [6]) is a maximal connected subgraph containing no cut of itself. For a given subgroup ?f of automorphism group of graph, we say that two are similar if a permutation of ?f sends one point into other. By the number of dissimilar points of a graph we mean number of equivalence classes of similar in it; analogously for lines, blocks, etc.
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