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1.
Characterization of reducible hexagons and fast decomposition of elementary benzenoid graphs
Andrej Taranenko, Aleksander Vesel, 2008, izvirni znanstveni članek

Opis: A benzenoid graph is a finite connected plane graph with no cut vertices in which every interior region is bounded by a regular hexagon of a side length one. A benzenoid graph G is elementary if every edge belongs to a 1-factor of G. A hexagon h of an elementary benzenoid graph is reducible, if the removal of boundary edges and vertices of h results in an elementary benzenoid graph. We characterize the reducible hexagons of an elementary benzenoid graph. The characterization is the basis for an algorithm which finds the sequence of reducible hexagons that decompose a graph of this class in ▫$O(n^2)$▫ time. Moreover, we present an algorithm which decomposes an elementary benzenoid graph with at most one pericondensed component in linear time.
Ključne besede: mathematics, graph theory, benzenoid graphs, 1-factor, hexagons, reducible hexagons, reducible face decomposition
Objavljeno: 07.06.2012; Ogledov: 986; Prenosov: 28
URL Povezava na celotno besedilo

2.
1-factors and characterization of reducible faces of plane elementary bipartite graphs
Andrej Taranenko, Aleksander Vesel, 2012, izvirni znanstveni članek

Opis: 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.
Ključne besede: mathematics, graph theory, plane elementary bipartite graph, reducible face, benzenoid graph
Objavljeno: 31.03.2017; Ogledov: 251; Prenosov: 92
.pdf Celotno besedilo (139,73 KB)
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