# The crossing number of the generalized Petersen graph $P[3k,k]$

Stanley Fiorini; John Baptist Gauci

Mathematica Bohemica (2003)

- Volume: 128, Issue: 4, page 337-347
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topFiorini, Stanley, and Gauci, John Baptist. "The crossing number of the generalized Petersen graph $P[3k,k]$." Mathematica Bohemica 128.4 (2003): 337-347. <http://eudml.org/doc/249227>.

@article{Fiorini2003,

abstract = {Guy and Harary (1967) have shown that, for $k\ge 3$, the graph $P[2k,k]$ is homeomorphic to the Möbius ladder $\{M_\{2k\}\}$, so that its crossing number is one; it is well known that $P[2k,2]$ is planar. Exoo, Harary and Kabell (1981) have shown hat the crossing number of $P[2k+1,2]$ is three, for $k\ge 2.$ Fiorini (1986) and Richter and Salazar (2002) have shown that $P[9,3]$ has crossing number two and that $P[3k,3]$ has crossing number $k$, provided $k\ge 4$. We extend this result by showing that $P[3k,k]$ also has crossing number $k$ for all $k\ge 4$.},

author = {Fiorini, Stanley, Gauci, John Baptist},

journal = {Mathematica Bohemica},

keywords = {graph; drawing; crossing number; generalized Petersen graph; Cartesian product; graph; drawing; crossing number; generalized Petersen graph; Cartesian product},

language = {eng},

number = {4},

pages = {337-347},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {The crossing number of the generalized Petersen graph $P[3k,k]$},

url = {http://eudml.org/doc/249227},

volume = {128},

year = {2003},

}

TY - JOUR

AU - Fiorini, Stanley

AU - Gauci, John Baptist

TI - The crossing number of the generalized Petersen graph $P[3k,k]$

JO - Mathematica Bohemica

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 128

IS - 4

SP - 337

EP - 347

AB - Guy and Harary (1967) have shown that, for $k\ge 3$, the graph $P[2k,k]$ is homeomorphic to the Möbius ladder ${M_{2k}}$, so that its crossing number is one; it is well known that $P[2k,2]$ is planar. Exoo, Harary and Kabell (1981) have shown hat the crossing number of $P[2k+1,2]$ is three, for $k\ge 2.$ Fiorini (1986) and Richter and Salazar (2002) have shown that $P[9,3]$ has crossing number two and that $P[3k,3]$ has crossing number $k$, provided $k\ge 4$. We extend this result by showing that $P[3k,k]$ also has crossing number $k$ for all $k\ge 4$.

LA - eng

KW - graph; drawing; crossing number; generalized Petersen graph; Cartesian product; graph; drawing; crossing number; generalized Petersen graph; Cartesian product

UR - http://eudml.org/doc/249227

ER -

## References

top- The crossing numbers of some generalized Petersen graphs, Math. Scand. 48 (1981), 184–188. (1981) MR0631334
- On the crossing number of generalized Petersen graphs, Ann. Discrete Math. 30 (1986), 225–242. (1986) Zbl0595.05030MR0861299
- 10.4153/CMB-1967-046-4, Canad. Math. Bull. 10 (1967), 493–496. (1967) MR0224499DOI10.4153/CMB-1967-046-4
- On the crossing numbers of ${S}_{m}\times {C}_{n}$, Čas. Pěst. Mat. 107 (1982), 225–230. (1982) MR0673046
- Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271–283. (1930)
- 10.1007/s003730200028, Graphs Combin. 18 (2002), 381–394. (2002) MR1913677DOI10.1007/s003730200028

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.