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On the characterizing properties of the circuit polynomial. (English) Zbl 0880.05072
The circuit polynomial of a graph was described in a paper by the first author in [Discrete Math. 25, 121-133 (1979; Zbl 0401.05057)]. In the present paper the authors show that the circuit polynomial characterizes many well-known families of graphs, including chains, stars, cycles, complete graphs, regular complete bipartite graphs, and wheels.

MSC:
05C75 Structural characterization of families of graphs
05C38 Paths and cycles
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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