scholarly journals Sharp upper bounds on the Clar number of fullerene graphs

2018 ◽  
Vol 38 (1) ◽  
pp. 155
Author(s):  
Yang Gao ◽  
Heping Zhang
Keyword(s):  
Upper Bounds ◽  
Clar Number ◽  
Fullerene Graphs

scholarly journals Some Bounds for the Kirchhoff Index of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yujun Yang
Keyword(s):  
Connected Graph ◽  
Planar Graphs ◽  
Independence Number ◽  
Clique Number ◽  
Upper Bounds ◽  
Electrical Network ◽  
Lower And Upper Bounds ◽  
Kirchhoff Index ◽  
Resistance Distance ◽  
Fullerene Graphs

The resistance distance between two vertices of a connected graphGis defined as the effective resistance between them in the corresponding electrical network constructed fromGby replacing each edge ofGwith a unit resistor. The Kirchhoff index ofGis the sum of resistance distances between all pairs of vertices. In this paper, general bounds for the Kirchhoff index are given via the independence number and the clique number, respectively. Moreover, lower and upper bounds for the Kirchhoff index of planar graphs and fullerene graphs are investigated.

An Upper Bound for the Clar Number of Fullerene Graphs

2006 ◽  
Vol 41 (2) ◽  
pp. 123-133 ◽  
Author(s):  
Heping Zhang ◽  
Dong Ye
Keyword(s):  
Upper Bound ◽  
Clar Number ◽  
Fullerene Graphs

ChemInform Abstract: Upper Bounds for the Clar Number of a Benzenoid Hydrocarbon.

ChemInform ◽  
2010 ◽  
Vol 23 (39) ◽  
pp. no-no
Author(s):  
P. HANSEN ◽  
M. ZHENG
Keyword(s):  
Upper Bounds ◽  
Benzenoid Hydrocarbon ◽  
Clar Number

Upper bounds for the Clar number of a benzenoid hydrocarbon

1992 ◽  
Vol 88 (12) ◽  
pp. 1621 ◽  
Author(s):  
Pierre Hansen ◽  
Maolin Zheng
Keyword(s):  
Upper Bounds ◽  
Benzenoid Hydrocarbon ◽  
Clar Number

scholarly journals Upper Bounds for Perfect Matchings in Pfaffian and Planar Graphs

10.37236/2845 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Afshin Behmaram ◽  
Shmuel Friedland
Keyword(s):  
Planar Graphs ◽  
Upper Bounds ◽  
Perfect Matchings ◽  
Pfaffian Graphs ◽  
Better Than ◽  
Fullerene Graphs

We give upper bounds on weighted perfect matchings in Pfaffian graphs. These upper bounds are better than Bregman's upper bounds on the number of perfect matchings. We show that some of our upper bounds are sharp for 3 and 4-regular Pfaffian graphs. We apply our results to fullerene graphs.

scholarly journals Extremal fullerene graphs with the maximum Clar number

2009 ◽  
Vol 157 (14) ◽  
pp. 3152-3173 ◽  
Author(s):  
Dong Ye ◽  
Heping Zhang
Keyword(s):  
Clar Number ◽  
Fullerene Graphs

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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