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Z-Transformation Graphs of Perfect Matchings of Hexagonal Systems
[chapter]
1988
Annals of Discrete Mathematics
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In this paper we introduce a new kind of transformation graph, namely Z-transformation graph of perfect matchings of hexagonal systems and observe some of its properties. ...
We define the Z-transformation graph Z(H) to be the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is ...
doi:10.1016/s0167-5060(08)70810-0
fatcat:6lpp6zaylrecvd4xwmbwu4byz4
Z-transformation graphs of perfect matchings of hexagonal systems
1988
Discrete Mathematics
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In this paper we introduce a new kind of transformation graph, namely Z-transformation graph of perfect matchings of hexagonal systems and observe some of its properties. ...
We define the Z-transformation graph Z(H) to be the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is ...
doi:10.1016/0012-365x(88)90233-6
fatcat:fedkfo5c5vh7fgyhmixp7ydao4
Hamilton paths in Z-transformation graphs of perfect matchings of hexagonal systems
1997
Discrete Applied Mathematics
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The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of ...
Let H be a hexagonal system. ...
The Z-transformation graph Z(H) [3, 4] is the graph where the vertices are the perfect matchings of H and where two perfect matchings Ml and M2 are joined by an edge provided their symmetric difference ...
doi:10.1016/s0166-218x(97)81447-3
fatcat:mqua2gi2sbbbng5wemqrusqexu
Plane elementary bipartite graphs
2000
Discrete Applied Mathematics
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Second, the concept of the Z-transformation graph Z(G) of a hexagonal system G (whose vertices represent the perfect matchings of G) is extended to a plane bipartite graph G and some results analogous ...
of G) and whose Z-transformation graphs Z(G) contain vertices of degree one. ? ...
In connection to resonant hexagons (or aromatic sextets), Z-transformation graphs of perfect matchings of hexagonal systems H were deÿned [27, 28] . ...
doi:10.1016/s0166-218x(00)00204-3
fatcat:m7zs3kflxzct3bu3zpme6xf5m4
Forcing faces in plane bipartite graphs
2008
Discrete Mathematics
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[Z-transformation graphs of perfect matchings of hexagonal systems, Discrete Math. 72 (1988) 405-415; Plane elementary bipartite graphs, Discrete Appl. ...
Using the tool of Z-transformation graphs developed by Zhang et al. ...
For a hexagonal system H, we proved in [2] that if H has a perfect matching M such that M is of degree two in Z(H ) and the two M-resonant hexagons are adjacent, then Z(H ) is a path. ...
doi:10.1016/j.disc.2007.05.025
fatcat:jwo7ln6cj5cmtbrpcw3mdkwft4
Page 1318 of Mathematical Reviews Vol. , Issue 90B
[page]
1990
Mathematical Reviews
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The paper under review defines the Z- transformation graph Z(H) of a hexagonal system H with at least one perfect matching to be the graph whose vertices are the perfect matchings of H such that two perfect ...
Trinajstié (Zagreb)
90b:92083 92A40 05C70 Zhang, Fu Ji (PRC-XINJ); Guo, Xiao Feng (PRC-XINJ); Chen, Rong Si (PRC-FZHU-FE) Z-transformation graphs of perfect matchings of hexagonal systems. ...
Z -transformation graphs of maximum matchings of plane bipartite graphs
2004
Discrete Applied Mathematics
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If G has a perfect matching, Z(G) andZ(G) are the usual Z-transformation graph and digraph. If G has neither isolated vertices nor perfect matching, then Z(G) is not connected. ...
Let G be a plane bipartite graph. The Z-transformation graph Z(G) and its orientationZ(G) on the maximum matchings of G are deÿned. ...
[6, 7] introduced a concept of Z-transformation graph on the set of perfect matchings of a hexagonal system: two vertices are adjacent provided that their corresponding perfect matchings only di er ...
doi:10.1016/s0166-218x(03)00305-6
fatcat:px437d5p2rhvbftq42gz6244ke
Forcing faces in plane bipartite graphs (II)
2013
Discrete Applied Mathematics
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Che and Z. Chen, Forcing hexagons in hexagonal systems, MATCH Commun. Math. Comput. Chem. 56 (2006) 649-668]. ...
We also give a new necessary and sufficient condition for a finite face of G to be forcing in terms of bridges in the Z -transformation graph Z (G) of G. ...
In 1995, Zhang and Li [15] gave characterizations for a hexagonal system with forcing edges, by using the concept of Z -transformation graph of a hexagonal system introduced by Zhang et al. in [14] ...
doi:10.1016/j.dam.2012.08.016
fatcat:sc6dnjvy2vbl7mquocacvqrsou
Z-transformation graphs of perfect matchings of plane bipartite graphs
2004
Discrete Mathematics
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The Z-transformation graph, ZF (G), of G with respect to a speciÿc set F of faces is deÿned as a graph on the perfect matchings of G such that two perfect matchings M1 and M2 are adjacent provided M1 and ...
Let G be a plane bipartite graph with at least two perfect matchings. ...
[11, 12] introduced the concept of Z-transformation graphs, Z(H ), of perfect matchings of hexagonal systems H and showed that the connectivity of Z(H ) is equal to the minimum degree. ...
doi:10.1016/s0012-365x(03)00319-4
fatcat:tcabyoigvnayjpsv33osi7w4ky
Page 6746 of Mathematical Reviews Vol. , Issue 2004i
[page]
2004
Mathematical Reviews
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(PRC-LAN; Lanzhou
Z-transformation graphs of maximum matchings of plane bipartite graphs. ...
The Z-transformation graph Z(G) of a plane graph G is defined as the simple graph whose vertices are the maximum matchings of G, two vertices being adjacent if and only if their symmetric difference is ...
A relation between Clar covering polynomial and cube polynomial
[article]
2012
arXiv
pre-print
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In this paper we find that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a one-to-one correspondence between the Clar ...
The Clar covering polynomial (also called Zhang-Zhang polynomial in some chemical literature) of a hexagonal system is a counting polynomial for some types of resonant structures called Clar covers, which ...
The resonance graph R(H) (also called Z-transformation graph) of a hexagonal system H was introduced independently by Gründler [8] , Zhang et al. [28, 29] and Randić [23, 24] . ...
arXiv:1210.5322v1
fatcat:4ucnt72miramzj7ixr4z5iahmy
Hexagonal systems with fixed bonds
1993
Discrete Applied Mathematics
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This decomposition can be used to simplify the procedure of finding Clar's formula, counting the number of Kekult structures and constructing the Z-transformation graph of a hexagonal system with fixed ...
By this algorithm we can decompose a hexagonal system into a number of regions consisting of fixed bonds and a number of normal subhexagonal systems. ...
Z-transformation graph for a hexagonal system with fixed bonds. ...
doi:10.1016/0166-218x(93)90133-9
fatcat:qlhokx3y2bfbrbpqh2f2uq26vq
On plane bipartite graphs without fixed edges
2007
Applied Mathematics Letters
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An edge of a graph H with a perfect matching is a fixed edge if it either belongs to none or to all of the perfect matchings of H . ...
These results extend results on generalized hexagonal systems from [F. Zhang, M. Zheng, Generalized hexagonal systems with each hexagon being resonant, Discrete Appl. Math. 36 (1992) 67-73]. ...
Acknowledgements The first author thanks Professor Hernán Abeledo (Engineering Management and Systems Engineering, The George Washington University, USA) for drawing his attention to research on hexagonal ...
doi:10.1016/j.aml.2006.08.014
fatcat:7a35ynajc5h4fluf2crgjcgeam
Asymptotic enumeration of perfect matchings in m-barrel fullerene graphs
[article]
2017
arXiv
pre-print
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In this paper we asymptotically count by two different methods the number of perfect matchings in m-barrel fullerene graphs, as the number of hexagonal layers is large, and show that the results are equal ...
After that we have additional k layers of hexagons. At the last circle m-pentagons connected to the second m-gon. ...
It is obvious that perfect matchings such a hexagonal graph on the cylinder with pentagonal faces on the boundary are in bijection with tilings of the cylinder with unit rhombi, where some of the rhombi ...
arXiv:1710.05156v1
fatcat:ywmao4defbdu7bw6s65dspetvm
Page 59 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
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The Z-transformation graph Z(H) is the graph where the vertices are the perfect match- ings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of ...
Michal Penn (IL-TECHMG; Haifa)
2000a:05164 05C70 05C90
Zhang, Lian Zhu (PRC-ZZTC; Zhangzhou)
The Z-transformation graph of perfect matchings of a catacondensed hexagonal system. (Chinese. ...
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