The domination number of graph is the smallest cardinality set G. A subset a vertex S G called if every element dominates G, meaning that not an connected and one distance from S. has become interesting research studies on several graphs k -connected such as circulant graphs, grids, wheels. This study aims to determine other k-connected Harary graph. method used pattern detection axiomatic dedu...

A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case Žpurely . atomic measures with a finite number of atoms , and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-d...

In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points Xn := {xi}ni=0 in R, the barycentric approximation of a convex function f is of the form:

Standard binary subdivision operators may generate surfaces with unbounded curvatures at points corresponding to extraordinary vertices. This defect can be removed by manipulating the eigenvalues of the subdivision operator to impose a bounded curvature spectrum. This procedure may enlarge the support of an extraordinary vertex beyond its two-ring. In the ternary subdivision setting, where mesh...

Shape artifacts, especially for convex input polyhedra, make Doo and Sabin’s generalization of bi-quadratic (bi-2) subdivision surfaces unattractive for general design. Rather than tuning the eigenstructure of the subdivision matrix, we improve shape by adding a point and enriching the refinement rules. Adding a guiding point can also yield a polar bi-2 subdivision algorithm. Both the augmented...