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VOLUME OF GRAPH POLYTOPES FOR THE PATH-STAR TYPE GRAPHS

  • Ju, Hyeong-Kwan (Department of Mathematics, Chonnam National University) ;
  • Seo, Soo-Jeong (Department of Mathematics, Chonnam National University)
  • Received : 2015.11.16
  • Accepted : 2015.12.08
  • Published : 2016.03.25

Abstract

The aim of this work is to compute the volume of the graph polytope associated with various type of finite simple graphs composed of paths and stars. Recurrence relations are obtained using the recursive volume formula (RVF) which was introduced in Lee and Ju ([3]). We also discussed the relationship between the volume of the graph polytopes and the number of linear extensions of the associated posets for given bipartite graphs.

Keywords

graph polytope;volume;generating function;path-star type graph

References

  1. M. Bona, H.-K. Ju and R. Yoshida, On the enumeration of a certain weighted graphs, Discrete Applied Math., 155(2007), 1481-1496. https://doi.org/10.1016/j.dam.2007.04.001
  2. H.-K. Ju, S. Kim and S.-J. Seo, On the Volume of Graph Polytopes, Honam Math. J. 37(2015), No.3, 361-376. https://doi.org/10.5831/HMJ.2015.37.3.361
  3. D. Lee and H.-K. Ju, Different volume computation methods of graph polytopes. Preprint(arXiv:1507.07623v1 [math.CO]), 2015, submitted.
  4. The On-Line Encyclopedia of Integer Sequences, published electronically at http://oeis.org.
  5. W. Rudin, Principles of Mathematical Analysis (3rd ed.), McGraw-Hill, 1976.
  6. G. Stachowiak, The number of linear extensions of bipartite graphs, Order, 5(1988), 257-259. https://doi.org/10.1007/BF00354893
  7. R. Stanley, Enumerative Combinatorics vol.1 (2nd ed.), Cambridge Univ. Press, Cambridge, 2012.