Author:
Madhavi Duggaraju Radha,Mazumdar Lipika
Abstract
Let G = (V,E) be a graph of order n. Let R be a commutative ring and I denote the set of all ideals of R. Let ? : E ? I be an edge labeling. A generalized spline of (G, ?) is a vertex labeling F : V ? R such that for each edge uv, F(u) ? F(v) ? ?(uv). The set R(G,) of all generalized splines of (G, ?) is an R-module. In this paper we determine conditions for a subset of R(G,?) to form a basis of R(G,?) for some classes of graphs.
Publisher
Informatics Publishing Limited
Reference15 articles.
1. S. Altinok and S. Sarioglan, Basis criteria for generalized spline modules via determinant, Discrete Math., 344 (2021), 112223.
2. S. Altinok and S. Sarioglan, Flow-up bases for generalized spline modules on arbitrary graphs, J. Algebra Appl. 20(10), 2150180 (2021).
3. M. Atiyah and I. MacDonald, Introduction To Commutative Algebra, Addison-Wesley, Reading, Mass. 1969.
4. L. J. Billera and L. L. Rose, A dimension series for multivariate splines, Discrete Comput. Geom., 6(2) (1991), 107–128.
5. N. Bowden and J. Tymoczko, Splines mod m, ArXiv e-prints (2015).