On median graphs and median grid graphs

نویسندگان

  • Sandi Klavzar
  • Riste Skrekovski
چکیده

Let G be a Q4-free median graph on n vertices and m edges. Let k be the number of equivalence classes of Djoković-Winkler’s relation Θ and let h be the number of Q3’s in G. Then we prove that 2n −m − k + h = 2. We also characterize median grid graphs in several different ways, for instance, they are the grid graphs with m− n + 1 squares. To obtain these results we introduce the notion of square-edges, i.e. edges contained in exactly one 4-cycle of a graph.

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عنوان ژورنال:
  • Discrete Mathematics

دوره 219  شماره 

صفحات  -

تاریخ انتشار 2000