In this paper, the crossing numbers of the Cartesian products of a specific 5-vertex graph with a star are given, and thus the result fills up the crossing number list of Cartesian products of all 5-vertex graphs with...In this paper, the crossing numbers of the Cartesian products of a specific 5-vertex graph with a star are given, and thus the result fills up the crossing number list of Cartesian products of all 5-vertex graphs with stars （presented by Marian Klesc）. In addition, we also give an up to date description of Cartesian products of 5-vertex graphs with stars, whose crossing numbers are known.展开更多
Most results on crossing numbers of graphs focus on some special graphs, such as the Cartesian products of small graphs with path, star and cycle. In this paper, we obtain the crossing number formula of Cartesian prod...Most results on crossing numbers of graphs focus on some special graphs, such as the Cartesian products of small graphs with path, star and cycle. In this paper, we obtain the crossing number formula of Cartesian products of wheel Wm with path Pn for arbitrary m ≥ 3 and n ≥ 1.展开更多
By connecting the 5 vertices of K_3 to other n vertices,we obtain a special family of graph denoted by H_n.This paper proves that the crossing number of H_n is Z(5,n)+ 2n+[n/2]+ 1, and the crossing number of Cartesian...By connecting the 5 vertices of K_3 to other n vertices,we obtain a special family of graph denoted by H_n.This paper proves that the crossing number of H_n is Z(5,n)+ 2n+[n/2]+ 1, and the crossing number of Cartesian products of Ks with star S_n is Z(5,n)+ 5n+[n/2]+ 1.展开更多
基金the National Natural Science Foundation of China （No. 10771062） the Fund for New Century Excellent Talents in University （No. NCET-07-0276）.
文摘In this paper, the crossing numbers of the Cartesian products of a specific 5-vertex graph with a star are given, and thus the result fills up the crossing number list of Cartesian products of all 5-vertex graphs with stars （presented by Marian Klesc）. In addition, we also give an up to date description of Cartesian products of 5-vertex graphs with stars, whose crossing numbers are known.
基金the National Natural Science Foundation of China （No. 10771062） and New Century Excellent Talents in University （No. 07-0276）.
文摘Most results on crossing numbers of graphs focus on some special graphs, such as the Cartesian products of small graphs with path, star and cycle. In this paper, we obtain the crossing number formula of Cartesian products of wheel Wm with path Pn for arbitrary m ≥ 3 and n ≥ 1.
基金the National Natural Science Foundation of China （No. 10771062） and New Century Excellent Talents in University.
文摘By connecting the 5 vertices of K_3 to other n vertices,we obtain a special family of graph denoted by H_n.This paper proves that the crossing number of H_n is Z(5,n)+ 2n+[n/2]+ 1, and the crossing number of Cartesian products of Ks with star S_n is Z(5,n)+ 5n+[n/2]+ 1.
