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Module Basis for Generalized Spline Modules
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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.
Keywords
Generalized Spline Modules, Dutch Windmill Graph, Isomorphic Graphs.
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