Graph Skewness
المؤلف:
Chia, G. L. and Sim, K. A
المصدر:
"On the Skewness of the Join of Graphs." Disc. Appl. Math. 161
الجزء والصفحة:
...
24-4-2022
1917
Graph Skewness
The skewness of a graph 
is the minimum number of edges whose removal results in a planar graph (Harary 1994, p. 124). The skewness is sometimes denoted 
(Cimikowski 1992).
A graph 
with 
has toroidal crossing number 
. (However, there exist graphs with 
that still have 
.)
satisfies
 |
(1)
|
where 
is the vertex count of 
and 
its edge count (Cimikowski 1992).
The skewness of a disconnected graph is equal to the sum of skewnesses of its connected components.
The skewness of a complete graph 
is given by
![mu(K_n)=<span style=]() {0 for n<=4; 1/2(n-3)(n-4) otherwise, " src="https://mathworld.wolfram.com/images/equations/GraphSkewness/NumberedEquation2.svg" style="height:57px; width:245px" /> |
(2)
|
of the complete bipartite graph 
by
 |
(3)
|
and of the hypercube graph 
by
![mu(Q_n)=<span style=]() {0 for n<=3; 2^n(n-2)-n·2^(n-1)+4 otherwise " src="https://mathworld.wolfram.com/images/equations/GraphSkewness/NumberedEquation4.svg" style="height:53px; width:278px" /> |
(4)
|
(Cimikowski 1992).
REFERENCES
Chia, G. L. and Sim, K. A. "On the Skewness of the Join of Graphs." Disc. Appl. Math. 161, 2405-2409, 2013.
Cimikowski, R. J. "Graph Planarization and Skewness. In Proceedings of the Twenty-third Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1992). Congr. Numer., 88, 21-32, 1992.
Harary, F. Problem 11.24 in Graph Theory. Reading, MA: Addison-Wesley, p. 124, 1994.
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