An algorithm for generating generalized splines on graphs such as complete graphs, complete bipartite graphs and hypercubes

Figures & data

Fig. 1 Example of a generalized spline on the 4-cycle $C_4$.

Fig. 2 Example of a generalized spline on the complete graph $K_4$.

Fig. 3 Example of generalized integer spline on the 3-cycle $C_3$.

Fig. 4 Generalized spline on $K_3$.

Fig. 5 Generalized spline on $K_4$.

Fig. 6 Generalized spline on $K_5$.

Fig. 7 Generalized splines on$K_{1,2}$ and $K_{2,1}$.

Fig. 8 Generalized spline on $K_{2,2}$.

Fig. 9 Generalized spline on $K_{3,3}$.

Fig. 10 Generalized spline on $K_{n_1,n_2}$.

Fig. 11 Hypercubes $Q_1$, $Q_2$ and $Q_3$.

Fig. 12 Hamiltonicity of hypercubes $Q_2$ and $Q_3$.

Fig. 13 Bipartite structure of Hypercubes $Q_2$ and $Q_3$.

Fig. 14 Graph of Hypercube $Q_4$.

Fig. 15 Bipartite structure and Hamiltonicity of Hypercube $Q_4$.