35 citations · 156 across the 42 of their papers we have counts for
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The resonance graphs of nanotubes and toroidal polyhexes
Lingmei Liang, Heping Zhang
Coronoid systems, nanotubes and toroidal polyhexes (or fullerenes) can all be regarded as carbon networks composed of carbon atoms linked in hexagonal shapes. The resonance graphs…
The resonance graphs of coronoid systems and nanotubes
Lingmei Liang, Heping Zhang
The resonance graph of a hexagonal system is connected, which shows that a perfect matching can be transformed into any other perfect matchings by a series of flips along hexagons.…
The matching extendability of optimal 2-planar graphs
Xinyao Li, Heping Zhang
A graph is 2-planar if it can be drawn in the plane such that each edge is crossed by at most two other edges. It is known that for a 2-planar graph , .…
2-extendability of (4,5,6)-fullerenes
Lifang Zhao, Heping Zhang
A (4,5,6)-fullerene is a plane cubic graph whose faces are only quadrilaterals, pentagons and hexagons, which includes all (4,6)- and (5,6)-fullerenes. A connected graph with a…
Cubic vertices of minimal bicritical graphs
Jing Guo, Hailun Wu, Heping Zhang
A graph with four or more vertices is called bicritical if the removal of any pair of distinct vertices of results in a graph with a perfect matching. A bicritical graph is…
Number of Matchings of Low Order in (4,6)-Fullerene Graphs
Zhi-Feng Wei, Heping Zhang
We obtain the formulae for the numbers of 4-matchings and 5-matchings in terms of the number of hexagonal faces in (4, 6)-fullerene graphs by studying structural classification of…