Minimal regular graphs with given girths and crossing numbers

Czasopismo

Discussiones Mathematicae Graph Theory

2004 | 24 | 2 | 223-237

Tytuł artykułu

Autorzy

G.L. Chia , C.S. Gan

Treść / Zawartość

Pełne teksty:

Warianty tytułu

Języki publikacji

Abstrakty

This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.

Słowa kluczowe

regular graphs girth crossing numbers

Kategorie tematyczne

Wydawca

De Gruyter Open

Czasopismo

Rocznik

2004

Tom

Numer

Strony

223-237

Opis fizyczny

Daty

wydano

2004

Twórcy

autor

G.L. Chia

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

autor

C.S. Gan

Faculty of Engineering and Technology, Multimedia University, 75450 Malacca, Malaysia

Bibliografia

[1] G. Chartrand and L. Lesniak, Graphs & Digraphs (Third edition), (Chapman & Hall, New York 1996).
[2] R.K. Guy and A. Hill, The crossing number of the complement of a circuit, Discrete Math. 5 (1973) 335-344, doi: 10.1016/0012-365X(73)90127-1.
[3] D.J. Kleitman, The crossing number of $K_{5,n}$, J. Combin. Theory B 9 (1970) 315-323, doi: 10.1016/S0021-9800(70)80087-4.
[4] M. Koman, On nonplanar graphs with minimum number of vertices and a given girth, Commentationes Math. Univ. Carolinae (Prague) 11 (1970) 9-17.
[5] D. McQuillan and R.B. Richter, On 3-regular graphs having crossing number at least 2, J. Graph Theory, 18 (1994) 831-839, doi: 10.1002/jgt.3190180807.
[6] M. Nihei, On the girths of regular planar graphs, Pi Mu Epsilon J. 10 (1995) 186-190.
[7] B. Richter, Cubic graphs with crossing number two, J. Graph Theory 12 (1988) 363-374, doi: 10.1002/jgt.3190120308.
[8] R.D. Ringeisen and L.W. Beineke, On the crossing numbers of products of cycles and graphs of order four, J. Graph Theory 4 (1980) 145-155, doi: 10.1002/jgt.3190040203.
[9] G.F. Royle, Graphs and multigraphs, in: C.J. Colbourn and J.H. Dinitz ed., The CRC Handbook of Combinatorial Designs, (CRC Press, New York, 1995) 644-653.
[10] G.F. Royle, Cubic cages, http://www.cs.uwa.edu.au/~gordon/cages/index.html.
[11] P.K. Wong, Cages - a survey, J. Graph Theory 6 (1982) 1-22, doi: 10.1002/jgt.3190060103.

Typ dokumentu

Bibliografia

Identyfikatory

DOI

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1227