A locally irregular graph is a graph whose adjacent vertices have distinct degrees, a regular graph is a graph where each vertex has the same degree and a locally regular graph is a graph where for every two adjacent vertices u, v, their degrees are equal. In this paper, we investigate the set of all problems which are related to decomposition of graphs into regular, locally regular and/or loca...

In this technical report the new version of the software Dgc tool is presented. This tool allows us to build up irregular graph pyramids by dual graph contraction. The graph pyramid consists of a stack of levels (pair of graphs), each of which has a primal level and its dual. Every successive level is a reduced version of the level below. Primal level and its dual represent a primal graph and i...

Let G be a group and CayP (G) < Sym(G) be the subgroup of all permutations that induce graph automorphisms on every Cayley graph of G. The group G is graphically abelian if the map ν : g → g−1 belongs to CayP (G); these groups have been classified. Also G is irregular if there exists σ ∈ CayP (G) such that σ = 1G, σ(1) = 1 and σ = ν. We show G is irregular if and only if G = Dic(A, I); every no...

An irregular coloring of a graph is a proper vertex coloring that distinguishes vertices in the graph either by their own colors or by the colors of their neighbors. In algebraic graph theory, graphs with a certain amount of symmetry can sometimes be specified in terms of a group and a smaller graph called a voltage graph. In [3], Radcliffe and Zhang found a bound for the irregular chromatic nu...

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

In this paper we present a method for the application of Convolutional Neural Network (CNN) operators for use in domains which exhibit irregular spatial geometry by use of the spectral domain of a graph Laplacian, Figure 1. This allows learning of localized features in irregular domains by defining neighborhood relationships as edge weights between vertices in graph G. By formulating the domain...

Edge Vertex Push Edge Edge The Problem: We want the fastest graph processing! • High-performance graph processing is very interesting for data science • High-performance computing is increasingly GPU/accelerator based • Mapping irregular (graph) algorithms to GPU is hard • Performance of irregular algorithms is data-dependent Thesis Goals • Quantify performance impact of data dependence • Model...

Many image analysis tasks lead to or make use of graph structures that are related through the analysis process with the planar layout of a digital image. This paper presents a theory that allows to build diierent types of hierarchies on top of such image graphs. The theory is based on the properties of a pair of dual image graphs that the reduction process should preserve, e.g. the structure o...

The graph-coloring metaphor leads to elegant algorithms for register allocation that have been shown to be quite effective for regular architectures with plenty of registers. Published attempts to make these algorithms applicable to architectures that are irregular in their use of registers have yielded several incompatible extensions that handle only a small subset of the irregularities seen i...