TY  - JOUR
ID  - Staš2023
LB  - Staš2023
AU  - Staš, Michal
AU  - Timková, Mária
TI  - The crossing numbers of join products of four graphs of order five with paths and cycles
ST  - The crossing numbers of join products of four graphs of order five with paths and cycles
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 6
SP  - 865
EP  - 883
DO  - https://doi.org/10.7494/OpMath.2023.43.6.865
UR  - https://doi.org/10.7494/OpMath.2023.43.6.865
AB  - The crossing number \(\mathrm{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings over all drawings of \(G\) in the plane. In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths and cycles. The crossing numbers of the join products \(G^\ast + P_n\) and \(G^\ast + C_n\) for the disconnected graph \(G^\ast\) consisting of the complete tripartite graph \(K_{1,1,2}\) and one isolated vertex are given, where \(P_n\) and \(C_n\) are the path and the cycle on \(n\) vertices, respectively. In the paper also the crossing numbers of \(H^\ast + P_n\) and \(H^\ast + C_n\) are determined, where \(H^\ast\) is isomorphic to the complete tripartite graph \(K_{1,1,3}\). Finally, by adding new edges to the graphs \(G^\ast\) and \(H^\ast\), we are able to obtain crossing numbers of join products of two other graphs \(G_1\) and \(H_1\) with paths and cycles.
KW  - graph
KW  - crossing number
KW  - join product
KW  - path
KW  - cycle
KW  - separating cycle
SN  - 1232-9274
ER  -