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Z-Transformation Graphs of Perfect Matchings of Hexagonal Systems
[chapter]

1988
*
Annals of Discrete Mathematics
*

In this paper we introduce a new kind

doi:10.1016/s0167-5060(08)70810-0
fatcat:6lpp6zaylrecvd4xwmbwu4byz4
*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 ...##
###
Z-transformation graphs of perfect matchings of hexagonal systems

1988
*
Discrete Mathematics
*

In this paper we introduce a new kind

doi:10.1016/0012-365x(88)90233-6
fatcat:fedkfo5c5vh7fgyhmixp7ydao4
*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 ...##
###
Hamilton paths in Z-transformation graphs of perfect matchings of hexagonal systems

1997
*
Discrete Applied Mathematics
*

The

doi:10.1016/s0166-218x(97)81447-3
fatcat:mqua2gi2sbbbng5wemqrusqexu
*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 ...##
###
Plane elementary bipartite graphs

2000
*
Discrete Applied Mathematics
*

Second, the concept

doi:10.1016/s0166-218x(00)00204-3
fatcat:m7zs3kflxzct3bu3zpme6xf5m4
*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] . ...##
###
Forcing faces in plane bipartite graphs

2008
*
Discrete Mathematics
*

[

doi:10.1016/j.disc.2007.05.025
fatcat:jwo7ln6cj5cmtbrpcw3mdkwft4
*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. ...##
###
Page 1318 of Mathematical Reviews Vol. , Issue 90B
[page]

1990
*
Mathematical Reviews
*

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
*

If G has a

doi:10.1016/s0166-218x(03)00305-6
fatcat:px437d5p2rhvbftq42gz6244ke
*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 ...##
###
Forcing faces in plane bipartite graphs (II)

2013
*
Discrete Applied Mathematics
*

Che and

doi:10.1016/j.dam.2012.08.016
fatcat:sc6dnjvy2vbl7mquocacvqrsou
*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] ...##
###
Z-transformation graphs of perfect matchings of plane bipartite graphs

2004
*
Discrete Mathematics
*

The

doi:10.1016/s0012-365x(03)00319-4
fatcat:tcabyoigvnayjpsv33osi7w4ky
*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. ...##
###
Page 6746 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

(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

In this paper we find that the Clar covering polynomial

arXiv:1210.5322v1
fatcat:4ucnt72miramzj7ixr4z5iahmy
*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] . ...##
###
Hexagonal systems with fixed bonds

1993
*
Discrete Applied Mathematics
*

This decomposition can be used to simplify the procedure

doi:10.1016/0166-218x(93)90133-9
fatcat:qlhokx3y2bfbrbpqh2f2uq26vq
*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. ...##
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On plane bipartite graphs without fixed edges

2007
*
Applied Mathematics Letters
*

An edge

doi:10.1016/j.aml.2006.08.014
fatcat:7a35ynajc5h4fluf2crgjcgeam
*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*...##
###
Asymptotic enumeration of perfect matchings in m-barrel fullerene graphs
[article]

2017
*
arXiv
*
pre-print

In this paper we asymptotically count by two different methods the number

arXiv:1710.05156v1
fatcat:ywmao4defbdu7bw6s65dspetvm
*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 ...##
###
Page 59 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

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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