Semiharmonic bicyclic graphs

نویسندگان

Stefan Grünewald

Dragan Stevanovic

چکیده

Classification of harmonic and semiharmonic graphs according to their cyclomatic number became of interest recently. All finite harmonic graphs with up to four independent cycles, as well as all finite semiharmonic graphs with at most one cycle were determined. Here, we determine all finite semiharmonic bicyclic graphs. Besides that, we present several methods to construct semiharmonic graphs from existing ones, and we apply one of these constructions to show that the number of semiharmonic graphs with fixed cyclomatic number k is infinite for every k. MSC Classification: 05C75

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