The crossing numbers of products of a 5-vertex graph with paths and cycles | Zendy

Marián Klešč | Zendy

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The crossing numbers of products of a 5-vertex graph with paths and cycles

Author(s) -

Marián Klešč

Publication year - 1999

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1085

Subject(s) - combinatorics , mathematics , cartesian product , vertex (graph theory) , crossing number (knot theory) , graph , cartesian coordinate system , stars , discrete mathematics , computer science , geometry , intersection (aeronautics) , engineering , aerospace engineering , computer vision

There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with “small” graphs. Let H be the 5-vertex graph defined from K5 by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H ×Pn and H ×Cn, showing that in the general case the corresponding crossing numbers are 3n−1, and 3n for even n or 3n + 1 if n is odd.

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