Podobno kot Cayleyevi grafi so tudi ▫$G$▫-grafi konstruirani iz grup. Predstavimo metodo za konstruiranje razširitvenih družin ▫$G$▫-grafov in jo uporabimo za konstruiranje novih razširitvenih družin ...neregularnih grafov. Ta tehnika temelji na odnosu med nekaterimi znanimi razširitvenimi družinami Cayleyjevih grafov in določenimi razširitvenimi družinami ▫$G$▫-grafov. Predstavimo tudi naketere druge lastnosti razširitvenih družin ▫$G$▫-grafov.
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