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Skewness of generalized Petersen graphs and related graphs |
Gek Ling CHIA( ), Chan Lye LEE |
| Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia |
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Abstract The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. In this paper, we determine the skewness of the generalized Petersen graph P(4k, k) and hence a lower bound for the crossing number of P(4k, k). In addition, an upper bound for the crossing number of P(4k, k) is also given.
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| Keywords
Skewness
generalized Petersen graph
crossing number
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Corresponding Author(s):
CHIA Gek Ling,Email:glchia@um.edu.my
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Issue Date: 01 June 2012
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| 1 |
Chia G L, Lee C L. Crossing numbers and skewness of some Generalized Petersen graphs. Lecture Notes in Comput Sci , 2005, 3330: 80-86
doi: 10.1007/978-3-540-30540-8_8
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| 2 |
Chia G L, Lee C L. Skewness and crossing numbers of graphs. Bull Inst Combin Appl , 2009, 55: 17-32
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| 3 |
Fiorini S, Gausi J B. The crossing number of the generalized Petersen graph P[3k, k]. Math Bohem , 2003, 128: 337-347
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| 4 |
Liu P C, Geldmacher R C. On the deletion of nonplanar edges of a graph. Congr Numer , 1979, 24: 727-738
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Salazar G. On the crossing numbers of loop networks and generalized Petersen graphs. Discrete Math , 2005, 302: 243-253
doi: 10.1016/j.disc.2004.07.036
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