Refinement operators for triangular meshes as used in subdivision schemes or remeshing are discussed. A numbering scheme is presented, covering all refinement operators that (topologically) map vertices onto vertices. Using this characterization, some special properties of n-adic and √ 3-subdivision are easy to see.

For a graph G and a proper coloring c : V (G) → {1, 2, . . . , k} of the vertices of G for some positive integer k , the color code of a vertex v of G (with respect to c ) is the ordered (k + 1) -tuple code(v) = (a0, a1, . . . , ak) where a0 is the color assigned to v and for 1 ≤ i ≤ k , ai is the number of vertices adjacent to v that are colored i . The coloring c is irregular if distinct vert...

A graph $G$ is called irregular if the degrees of all its vertices are not same. said to be \textit{Stepwise Irregular} (SI) difference any two adjacent always 1 (one). This paper deals with \textit{2-Stepwise (2-SI) graphs in which every pair differ by 2. Here we discuss some properties 2-SI and generalize them for $k$-SI imbalance edge $k$. Besides, also compute bounds irregularity Albertson ...

Network science makes heavy use of simulation models and calculations based upon graph-oriented data structures that are intrinsically highly irregular in nature. The key to efficient use of data-parallel and multi-core parallelism on graphical processing units (GPUs) and CPUs is often to optimise the data layout and to exploit distributed memory locality with processing elements. We describe w...

Computation of homology generators using an irregular graph pyramid can significantly increase performance compared to the classical methods. First results in 2D exist and show the advantages of the method. The generators are computed in upper levels of pyramid where it is known that the graphs contains a number of self loops and multiple edges product of the contraction processes. Using a stra...

Pattern Recognition and Image Processing Group Institute of Computer Aided Automation Vienna University of Technology Treitlstr. 3/1832 A-1040 Vienna AUSTRIA Phone: +43 (1) 58801-18351 Fax: +43 (1) 5054668 E-mail: [email protected], [email protected] URL: http://www.prip.tuwien.ac.at/ PRIP-TR-54 January 29, 1999 Dual Contraction of Combinatorial Maps Luc Brun and Walter Kropatsch1 Abs...

An undirected simple graphG is locally irregular if adjacent vertices ofG have different degrees. An edge-colouring φ ofG is locally irregular if each colour class of φ induces a locally irregular subgraph of G. The irregular chromatic index χirr(G) of G is the least number of colours used by a locally irregular edge-colouring of G (if any). We show that the problem of determining the irregular...

Locality behavior study is crucial for achieving good performance for irregular problems. Graph algorithms with large, sparse inputs, for example, oftentimes achieve only a tiny fraction of the potential peak performance on current architectures. Compared with most numerical algorithms graph algorithms lay higher pressure on the memory system. In this paper, using the minimum spanning tree prob...

It is essential to predict crowd flow precisely in a city, which practically partitioned into irregular regions based on road networks and functionality. However, prior works mainly focus grid-based prediction, where city divided many regular grids. Although Convolutional Neural Netwok (CNN) powerful capture spatial dependence from Euclidean data, it fails tackle non-Euclidean reflect the corre...