We call a simple graph highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we examine the degree sequences of highly irregular graphs. We give necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a highly irregular graph.

A graph G is locally irregular if adjacent vertices of G have different degrees. A k-edge colouring φ of G is locally irregular if each of the k colours 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 ofG (if any). We show that determining whether χirr(G) = 2 is NP-complete, even...

The Bounded Irregular Pyramid (BIP) is a hierarchical structure for image representation whose aim is to combine concepts from regular and irregular pyramids. The data structure is a combination of the simplest regular and irregular structures: the 2× 2/4 regular one and the simple graph representation. However, simple graphs only take into account adjacency relationships, being unable to corre...

This paper presents the Graph Analytics Repository for Designing Next-generation Accelerators (GARDENIA), a benchmark suite for studying irregular algorithms on massively parallel accelerators. Existing generic benchmarks for accelerators have mainly focused on high performance computing (HPC) applications with limited control and data irregularity, while available graph analytics benchmarks do...

We consider only finite undirected graphs without loops or multiple edges. For terminology and notation not defined here we refer the reader to Bondy and Murty’s textbook [6]. In this note we investigate irregularity measures of graphs. A graph is regular if all its vertices have the same degree, otherwise it is irregular. However, it is of interest to measure how irregular it is. Several appro...

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...