The Crossing Numbers of Join of Paths and Cycles with Two Graphs of Order Five

  • Marián Klešč
  • Štefan Schrötter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. Only few results concerning crossing numbers of graphs obtained as join product of two graphs are known. There are collected the exact values of crossing numbers for join of all graphs of at most four vertices with paths and cycles. In the paper, we extend these results. For two special graphs G on five vertices, we give the crossing numbers of the join products G + D n , G + P n , and G + C n , where D n consists on n isolated vertices, P n and C n are the path and cycle on n vertices, respectively.


graph drawing crossing number join product path cycle 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marián Klešč
    • 1
  • Štefan Schrötter
    • 1
  1. 1.Department of Mathematics and Theoretical Informatics, FEITechnical University of KošiceSlovak Republic

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