Resonance graphs of catacondensed even ring systems
نویسندگان
چکیده
منابع مشابه
Resonance graphs of catacondensed even ring systems are median
Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric difference is a bounded face of G. For a class of graphs containing the chemically important catacondensed benzenoid graphs we show that the resonance graphs are median. In particular, if G belongs to this class, R(G) has an is...
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The Fibonacci dimension fdim(G) of a graph G was introduced in [1] as the smallest integer d such that G admits an isometric embedding into Γd, the d-dimensional Fibonacci cube. The Fibonacci dimension of the resonance graphs of catacondensed benzenoid systems is studied. This study is inspired by the fact, that the Fibonacci cubes are precisely the resonance graphs of a subclass of the catacon...
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The vertex set of the resonance graph of a hexagonal graph G consists of 1-factors of G, two 1-factors being adjacent whenever their symmetric difference forms the edge set of a hexagon of G. A decomposition theorem for the resonance graphs of catacondensed hexagonal graph is proved. The theorem intrinsically uses the Cartesian product of graphs. A canonical binary coding of 1-factors of cataco...
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The algebraic Kekulé structure of a finite catacondensed benzenoid graph with h hexagons is described by a binary code of length h. The procedure can be reversed, any (algebraic) Kekulé structure can be recovered from its binary code. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملA min-max result on catacondensed benzenoid graphs
The resonance graph of a benzenoid graph G has the 1-factors of G as vertices, two 1-factors being adjacent if their symmetric difference forms the edge set of a hexagon of G. It is proved that the smallest number of elementary cuts that cover a catacondensed benzenoid graph equals the dimension of a largest induced hypercube of its resonance graph.
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2020
ISSN: 0096-3003
DOI: 10.1016/j.amc.2020.125064