TY  - JOUR
ID  - Staš2020
LB  - Staš2020
AU  - Staš, Michal
TI  - On the crossing numbers of join products of five graphs of order six with the discrete graph
ST  - On the crossing numbers of join products of five graphs of order six with the discrete graph
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 3
SP  - 383
EP  - 397
DO  - https://doi.org/10.7494/OpMath.2020.40.3.383
UR  - https://doi.org/10.7494/OpMath.2020.40.3.383
AB  - The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product \(G^{\ast} + D_n\), where the disconnected graph \(G^{\ast}\) of order six consists of one isolated vertex and of one edge joining two nonadjacent vertices of the \(5\)-cycle. In our proof, the idea of cyclic permutations and their combinatorial properties will be used. Finally, by adding new edges to the graph \(G^{\ast}\), the crossing numbers of \(G_i+D_n\) for four other graphs \(G_i\) of order six will be also established.
KW  - graph
KW  - drawing
KW  - crossing number
KW  - join product
KW  - cyclic permutation
SN  - 1232-9274
ER  -