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1.
On plane bipartite graphs without fixed edges
Khaled Salem, Sandi Klavžar, 2007, original scientific article

Abstract: Povezava grafa ▫$H$▫, ki premore vsaj eno popolno prirejanje, je fiksna povezava, če bodisi pripada vsem popolnim prirejanjem v ▫$H$▫ bodisi nobenemu popolnemu prirejanju. Dokazano je, da je povezan, ravninski, dvodelni graf brez fiksnih povezav natanko tedaj, ko je rob vsakega lica alternirajoči cikel. Nadalje je poliheksagonalen fragment brez fiksnih povezav natanko tedaj, ko so robovi neskončnega lica in vseh nešesterokotniških lic alternirajoči cikli. Dobljeni rezultati predstavljajo razširitev rezultatov iz [F. Zhang, M. Zheng, Generalized hexagonal systems with each hexagon being resonant, Discrete Appl. Math. 36 (1992) 67-73] na posplošene haksagonalne sisteme.
Keywords: matematika, teorija grafov, popolno prirejanje, fiksna povezava, alternirajoči cikel, dvodelni ravninski graf, poliheksagonalen fragment, posplošen heksagonalen sistem, mathematics, graph theory, perfect matching, fixed edge, alternating cycle, plane bipartite graph, polyhex fragment, generalized hexagonal system
Published: 10.07.2015; Views: 435; Downloads: 50
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2.
1-factors and characterization of reducible faces of plane elementary bipartite graphs
Andrej Taranenko, Aleksander Vesel, 2012, original scientific article

Abstract: As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekulé structures (1-factors). A bipartite graph ▫$G$▫ is called elementary if ▫$G$▫ is connected and every edge belongs to a 1-factor of ▫$G$▫. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given. A peripheral face ▫$f$▫ of a plane elementary graph is reducible, if the removal of the internal vertices and edges of the path that is the intersection of ▫$f$▫ and the outer cycle of ▫$G$▫ results in an elementary graph. We characterize the reducible faces of a plane elementary bipartite graph. This result generalizes the characterization of reducible faces of an elementary benzenoid graph.
Keywords: mathematics, graph theory, plane elementary bipartite graph, reducible face, benzenoid graph
Published: 31.03.2017; Views: 376; Downloads: 207
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