@article{, AUTHOR = {Kle¹č, Mariįn and Petrillovį, Jana}, TITLE = {The crossing numbers of products of path with graphs of order six}, JOURNAL = {Discuss. Math. Graph Theory}, FJOURNAL = {Discussiones Mathematicae Graph Theory}, VOLUME = {33}, YEAR = {2013}, NUMBER = {3}, PAGES = {571582}, ISSN = {12343099}, ABSTRACT = {The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path $P_n$ of length $n$, the crossing numbers of Cartesian products $G \Box P_n$ for all connected graphs $G$ on five vertices are also known. In this paper, the crossing numbers of Cartesian products $G \Box P_n$ for graphs $G$ of order six are studied. Let $H$ denote the unique tree of order six with two vertices of degree three. The main contribution is that the crossing number of the Cartesian product $H \Box P_n$ is $2(n1)$. In addition, the crossing numbers of $G \Box P_n$ for fourty graphs $G$ on six vertices are collected.}, }
