Free products of networks and free symmetrizers of graphs

Connected locally finite vertex-symmetric graphs, also called networks, are the subject of the article. The operation of a free product, preserving the vertex symmetry of graphs, is introduced. Properties of free products are studied, and a connection with free products of groups is established. A class of networks, called free symmetrizers of graphs, in some respects analogues of free products, is introduced. Their properties and a relation to free products and graphs of groups are studied.
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