Resonance graphs of catacondensed even ring systems are median
Klavžar, Sandi ; Žigert, Petra ; Brinkmann, Gunnar
Naj bo ▫$G$▫ 2-povezan graf vložen v ravnino. Točke resonančnega grafa ▫$R(G)$▫ so 1-faktorji grafa ▫$G$▫, pri čemer sta 1-faktorja sosednja, če tvori njuna simetrična razlika omejeno lice grafa ...▫$G$▫. Dokazano je, da so resonančni grafi razreda grafov, ki vsebujejo kemijsko pomembne katakondenzirane benzenoidne grafe, medianski. V posebnem; če je ▫$G$▫ graf tega razreda, potem ima ▫$R(G)$▫ izometrično vložitev v ▫$Q_f$▫, kjer je ▫$f$▫ število omejenih lic grafa ▫$G$▫.
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