ALTERNATIVE PROOF ON THE CROSSING NUMBER OF K1,1,3,N

Acta Electrotechnica et Informatica

卷:19

Michal STAS¹ 

[1] Department of Mathematics and Theoretical Informatic, Faculty of Electrical Engineering and Informatics, Technical University of Kosice, Bozeny Nemcovej 32, 042 00 Kosice, Slovakia;

关键词: graph;    drawing;    crossing number;    join product;   

DOI  :  10.15546/aeei-2019-0003

来源: DOAJ

【 摘 要 】

The main aim of the paper is to give the crossing number of join product G+Dn for the connected graph G of order five isomorphicwith the complete tripartite graph K1,1,3, where Dn consists on n isolated vertices. The proof of the crossing number of K1,1,3,n waspublished by very rather unclear discussion of cases by Ho in [5]. In our proofs, it will be extend the idea of the minimum numbersof crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph G onto the setof subgraphs which cross the edges of the graph G exactly once. The methods used in the paper are new, and they are based oncombinatorial properties of cyclic permutations. Finally, by adding one edge to the graph G, we are able to obtain the crossing numberof the join product with the discrete graph Dn for one new graph

【 授权许可】

Unknown