[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b170821

DIFFERENT VOLUME COMPUTATIONAL METHODS OF GRAPH POLYTOPES

Ju, Hyeong-Kwan (Department of Mathematics Chonnam National University)
Kim, Sangwook (Department of Mathematics Chonnam National University)
Lee, Daeseok (KAIST)

Publication Information

Bulletin of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1405-1417 More about this Journal

Abstract

The aim of this work is to introduce several different volume computational methods of graph polytopes associated with various types of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and most useful to compute the volume of the graph polytope for an arbitrary finite simple graph.

Keywords

graph polytope; volume; generating function;

Citations & Related Records

Reference

1	M. Beck and S. Robins, Computing the Continuous Discretely, Undergraduate Texts in Mathematics, Springer, New York, 2007.
2	M. Bona, H.-K. Ju, and R. Yoshida, On the enumeration of certain weighted graphs, Discrete Appl. Math. 155 (2007), no. 11, 1481-1496. DOI
3	N. D. Elkies, On the sums ${\Sigma}^{\infty}_{{\kappa}=-{\infty}(4k+1)^{-n}$ , Amer. Math. Monthly 110 (2003), no. 7, 561-573. DOI
4	V. Hutson, J. S. Pym, and M. J. Cloud, Applications of Functional Analysis and Operator Theory, second edition, Mathematics in Science and Engineering, 200, Elsevier B. V., Amsterdam, 2005.
5	H.-K. Ju, S. Kim, and S.-J. Seo, On the volume of graph polytopes, Honam Math. J. 37 (2015), no. 3, 361-376. DOI
6	W. Rudin, Principles of Mathematical Analysis, third edition, McGraw-Hill Book Co., New York, 1976.
7	R. P. Stanley, Enumerative Combinatorics. Volume 1, second edition, Cambridge Studies in Advanced Mathematics, 49, Cambridge University Press, Cambridge, 2012.