A generalization of chromatic polynomial of a graph subdivision

被引：0
作者：
D. M. Cardoso
M. E. Silva
J. Szymański
机构：
[1] Department of Mathematics, University of Aveiro, Aveiro
[2] Department of Discrete Mathematics, Adam Mickiewicz University, Poznań
来源：
Journal of Mathematical Sciences | 2012年 / 182卷 / 2期
关键词：
Complete Graph; Nonempty Subset; Chromatic Number; Simple Graph; Monic Polynomial;
D O I：
10.1007/s10958-012-0745-z
中图分类号：
学科分类号：
摘要：
Considering the partitions of a set into nonempty subsets, we obtain an expression for the number of all partitions of a given type. The chromatic polynomial of a graph subdivision is generalized, considering two sets of colors, and a general explicit expression is obtained for this generalization. Using these results, we determine the generalized chromatic polynomial for the particular case of complete graph subdivision. © 2012 Springer Science+Business Media, Inc.
引用
收藏
页码：246 / 254
页数：8
相关论文
共 6 条
  • [1] Berge C., Graphs, (1985)
  • [2] Birkhoff G.D., Lewis D., Chromatic polynomials, Trans. Am. Math. Soc., 60, pp. 355-451, (1946)
  • [3] Cardoso D.M., Szymanski J., Rostami M., Matemática Discreta: Combinatória, Teoria Dos Grafos E Algoritmos, (2008)
  • [4] Diestel R., Graph Theory, (1997)
  • [5] Herzberg A.M., Murty M.R., Sudoku squares and chromatic polynomials, Notices Am. Math. Soc., 54, 6, pp. 708-717, (2007)
  • [6] Stanley R.P., Enumerative Combinatorics, 1, (1997)
1