On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 3, p. 583.

Voir la notice de l'article dans European Digital Mathematics Library

The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of crossing numbers were obtained. The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. Moreover, except of six graphs, the crossing numbers of Cartesian products G⃞K1,n for all other connected graphs G on five vertices are known. In this paper we are dealing with the Cartesian products of stars with graphs on six vertices. We give the exact values of crossing numbers for some of these graphs and we summarise all known results concerning crossing numbers of these graphs. Moreover, we give the crossing number of G1⃞T for the special graph G1 on six vertices and for any tree T with no vertex of degree two as well as the crossing number of K1,n⃞T for any tree T with maximum degree five.
Classification : 05C10, 05C38
Mots-clés : graph, drawing, crossing number, Cartesian product, join product, star 
@article{DMGT_2013__33_3_267804,
     author = {Mari\'an Kle\v{s}\v{c} and \v{S}tefan Schr\"otter},
     title = {On the {Crossing} {Numbers} of {Cartesian} {Products} of {Stars} and {Graphs} of {Order} {Six}},
     journal = {Discussiones Mathematicae Graph Theory},
     pages = {583},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {2013},
     zbl = {1274.05098},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_3_267804/}
}
TY  - JOUR
AU  - Marián Klešč
AU  - Štefan Schrötter
TI  - On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
JO  - Discussiones Mathematicae Graph Theory
PY  - 2013
SP  - 583
VL  - 33
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_3_267804/
LA  - en
ID  - DMGT_2013__33_3_267804
ER  - 
%0 Journal Article
%A Marián Klešč
%A Štefan Schrötter
%T On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
%J Discussiones Mathematicae Graph Theory
%D 2013
%P 583
%V 33
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_3_267804/
%G en
%F DMGT_2013__33_3_267804
Marián Klešč; Štefan Schrötter. On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 3, p. 583. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_3_267804/