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Uniform resource networks. I: Complete graphs. (English. Russian original) Zbl 1187.90073
Autom. Remote Control 70, No. 11, 1889-1900 (2009); translation from Avtom. Telemekh. 2009, No. 11, 136-147 (2009).
Summary: A bidirectional resource network is a directed graph in which any two vertices \(\upsilon _i , \upsilon _j\) are either not adjacent or are connected by a pair of edges \((\upsilon _i , \upsilon _j ), (\upsilon _j , \upsilon _i )\). Non-negative numbers (resources) are assigned to vertices. The rules of functioning for such networks are formulated and processes of resource distribution in bidirectional networks represented by complete graphs are considered. It is shown that limit states of such networks do not depend on initial resource distributions.

MSC:
90B10 Deterministic network models in operations research
05C90 Applications of graph theory
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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