TY  - JOUR
ID  - Staš2022
LB  - Staš2022
AU  - Staš, Michal
AU  - Švecová, Mária
TI  - The crossing numbers of join products of paths with three graphs of order five
ST  - The crossing numbers of join products of paths with three graphs of order five
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 4
SP  - 635
EP  - 651
DO  - https://doi.org/10.7494/OpMath.2022.42.4.635
UR  - https://doi.org/10.7494/OpMath.2022.42.4.635
AB  - The main aim of this paper is to give the crossing number of the join product \(G^\ast+P_n\) for the disconnected graph \(G^\ast\) of order five consisting of the complete graph \(K_4\) and one isolated vertex, where \(P_n\) is the path on \(n\) vertices. The proofs are done with the help of a lot of well-known exact values for the crossing numbers of the join products of subgraphs of the graph \(G^\ast\) with the paths. Finally, by adding new edges to the graph \(G^\ast\), we are able to obtain the crossing numbers of the join products of two other graphs with the path \(P_n\).
KW  - graph
KW  - crossing number
KW  - join product
KW  - cyclic permutation
KW  - path
SN  - 1232-9274
ER  -