Octree Splitting We extend the irregular pyramid segmentation scheme to three dimensional (3D) digital space and we call it hyper-irregular pyramid segmentation. Based on this segmentation scheme, a 3D texture image is split into partitions recursively based on octree structure. The testure features are calculated based on 3D gray level spatial dependency measurement. The octree is subsequently...

A cycle C of length k is extendable if there is a cycle C′ of length k+1 with V (C) ⊂ V (C′). A graph G = (V,E) of order n is cycle extendable when every cycle C of length k < n is extendable. A chordal graph is a spider intersection graph if it admits an intersection representation which consists of subtrees of a sub-divided star (or spider). In 1990, Hendry conjectured that all hamiltonian ch...

In the paper retiming of DSP algorithms exhibiting multirate behavior is treated. Using the non-ordinary marked graph model and the reachability theory, we provide a new condition for valid retiming of multirate graphs. We show that for a graph with n nodes the reachability condition can be split into the reachability condition for the topologically-equivalent unit-rate graph (all rates set to ...

Chordal graph shelling antimatroids have received little attention with regard to their combinatorial properties and related optimization problems, as compared to the case of poset shelling antimatroids. Here we consider a special case of these antimatroids, namely the split graph shelling antimatroids. We show that the feasible sets of such an antimatroid relate to some poset shelling antimatr...

This paper deals with different chain graph interpretations and the relations between them in terms of representable independence models. Specifically, we study the Lauritzen-Wermuth-Frydenberg, Andersson-Madigan-Pearlman and multivariate regression interpretations and present the necessary and sufficient conditions for when a chain graph of one interpretation can be perfectly translated into a...

Given an undirected graph G = (V,E) and two positive integers k and d, we are interested in finding a set of edges (resp. non-edges) of size at most k to delete (resp. to add) in such a way that the chromatic number (resp. stability number) in the resulting graph will decrease by at least d compared to the original graph. We investigate these two problems in various classes of graphs (split gra...

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1, . . . , m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K2 has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomp...

The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D, and they form the distance spectrum of G. A graph is called distance integral if its distance spectrum consists entirely of integers. We show that no nontrivial tree can be distance integral. We characterize distance integral graphs in the classes of graphs similar to complete split graphs, which, toge...

A method to solve oversegmentation and undersegmentation in a region-based correspondence process is presented. The approach is based on performing a preprocessing step before using existing graph based methods. This preprocessing tries to assess the possible split regions in each image, with respect to the corresponding image, and form merge regions that could map better with regions in the ot...

Z-mapping graph is a balanced bipartite graph G of a digraph D by split each vertex of D into a pair of vertices of G. Based on the property of the G, it is proved that if D is strong connected and G is Hamiltonian, then D is Hamiltonian. It is also proved if D is Hamiltonian, then G contains at least a perfect matching. Thus some existence sufficient conditions for Hamiltonian digraph and Hami...