scholarly journals On k-Resonant Fullerene Graphs

2009 ◽  
Vol 23 (2) ◽  
pp. 1023-1044 ◽  
Author(s):  
Dong Ye ◽  
Zhongbin Qi ◽  
Heping Zhang
Keyword(s):  
Fullerene Graphs

Distance-restricted matching extendability of fullerene graphs

2017 ◽  
Vol 56 (2) ◽  
pp. 606-617
Author(s):  
Michitaka Furuya ◽  
Masanori Takatou ◽  
Shoichi Tsuchiya
Keyword(s):  
Matching Extendability ◽  
Fullerene Graphs

scholarly journals Computing the bipartite edge frustration of fullerene graphs

2007 ◽  
Vol 155 (10) ◽  
pp. 1294-1301 ◽  
Author(s):  
Tomislav Došlić ◽  
Damir Vukičević
Keyword(s):  
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.

scholarly journals Cyclic edge-cuts in fullerene graphs

2007 ◽  
Vol 44 (1) ◽  
pp. 121-132 ◽  
Author(s):  
František Kardoš ◽  
Riste Škrekovski
Keyword(s):  
Fullerene Graphs

Automorphism Group and Fixing Number of (3,6)– and (4, 6)–Fullerene Graphs

2014 ◽  
Vol 45 ◽  
pp. 113-120 ◽  
Author(s):  
F. Koorepazan-Moftakhar ◽  
A.R. Ashrafi ◽  
Z. Mehranian ◽  
M. Ghorbani
Keyword(s):  
Automorphism Group ◽  
Fullerene Graphs

A note on the cyclical edge-connectivity of fullerene graphs

2007 ◽  
Vol 43 (1) ◽  
pp. 134-140 ◽  
Author(s):  
Zhongbin Qi ◽  
Heping Zhang
Keyword(s):  
Edge Connectivity ◽  
Fullerene Graphs

scholarly journals On the Wiener Complexity and the Wiener Index of Fullerene Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1071 ◽  
Author(s):  
Andrey A. Dobrynin ◽  
Andrei Yu Vesnin
Keyword(s):  
Mathematical Models ◽  
Wiener Index ◽  
The Other ◽  
Graph Invariant ◽  
Calculation Results ◽  
Local Graph ◽  
Sum Of Distances ◽  
Fullerene Graphs

Fullerenes are molecules that can be presented in the form of cage-like polyhedra, consisting only of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex v of a graph is a local graph invariant defined as the sum of distances from v to all the other vertices. The number of different vertex transmissions is called the Wiener complexity of a graph. Some calculation results on the Wiener complexity and the Wiener index of fullerene graphs of order n ≤ 232 and IPR fullerene graphs of order n ≤ 270 are presented. The structure of graphs with the maximal Wiener complexity or the maximal Wiener index is discussed, and formulas for the Wiener index of several families of graphs are obtained.

Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes

2020 ◽  
Vol 23 ◽  
Author(s):  
Ayesha Shabbir ◽  
Muhammad Faisal Nadeem ◽  
Mohammad Ovais ◽  
Faraha Ashraf ◽  
Sumiya Nasir
Keyword(s):  
Graph Theory ◽  
Lower Bound ◽  
Coding Theory ◽  
Disjoint Union ◽  
Fullerene Molecule ◽  
Graph Labeling ◽  
Fullerene Graph ◽  
Theoretical Concepts ◽  
Large Numbers ◽  
Fullerene Graphs

Aims and Objective: A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule or simply a fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory where graph theoretical concepts used to study physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory which has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry and in many other fields. For example, in chemistry vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks. Method and Results: In terms of graphs vertices represent atoms while edges stand for bonds between atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons. Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and providing their exact values. Conclusion: The lower bound for tvs (tes) depending on the number of vertices, minimum and maximum degree of a graph exists in literature while to get different weights one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound we close the case for (3,6)-fullerene graphs.

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