This paper presents an algorithm for obtaining a constrained Delaunay triangulation from a given planar graph. The main advantage towards other algorithms is that I use an efficient Žalik’s algorithm, using a plane subdivison for obtaining a Delaunay triangulation. It is used for insertion of points into existing triangulation. The other part of algorithm presents a method for inserting edges, ...

We present a method for estimating functions on topologically and/or geometrically complex surfaces from possibly noisy observations. Our approach is an extension of spline smoothing, using a Þnite element method. The paper has a substantial tutorial component: we start by reviewing smoothness measures for functions deÞned on surfaces, simplicial surfaces and differentiable structures on such s...

Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...

Let G = (V, E) be a finite, simple and undirected graph having v = |V (G)| and e = |E(G)|. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) → {0, 1, 2, . . . , 2q−1} such that, when each edge xy is assigned the label |f(x)−f(y)|, the resulting edge labels are {1, 3, 5, . . . , 2q−1}. Motivated by the work of Z. Gao [6], we have defined odd graceful labeling f...

The selection of insecticide resistance in malaria vectors has the potential to compromise any insecticide-based vector control programme. To ensure that the insecticides used for indoor residual spraying and insecticide-treated nets in Zambia remain effective and their choice is evidence based, insecticide resistance surveillance and monitoring are essential. This study assessed and compared t...

A fundamental problem in network science is the normalization of topological or physical distance between vertices, that requires understanding range variation unnormalized distances. Here we investigate limits linear arrangements vertices trees. In particular, various problems on sum edge lengths trees a fixed size: minimum and maximum value for specific trees, classes (bistar caterpillar tree...

The aim of this paper is to present some odd graceful graphs. In particular we show that an odd graceful labeling of the all subdivision of double triangular snakes ( 2 k ∆ -snake ). We also prove that the all subdivision of 2 1 m∆ -snake are odd graceful. Finally, we generalize the above two results (the all subdivision of 2 k m∆ -snake are odd graceful).