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VOLUME OF GRAPH POLYTOPES FOR THE PATH-STAR TYPE GRAPHS
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  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 1,  2016, pp.71-84
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.1.71
 Title & Authors
VOLUME OF GRAPH POLYTOPES FOR THE PATH-STAR TYPE GRAPHS
Ju, Hyeong-Kwan; Seo, Soo-Jeong;
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 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;
 Language
English
 Cited by
 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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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R. Stanley, Enumerative Combinatorics vol.1 (2nd ed.), Cambridge Univ. Press, Cambridge, 2012.