Let G = (X, Y; E) be a balanced bipartite graph of order 2n. The path-cover number pc(H) of a graph H is the minimum number of vertex-disjoint paths that use up all the vertices of H. S ⊆ V(G) is called a balanced set of G if |S ∩ X| = |S ∩ Y|. In this paper, we will give some sufficient conditions for a balanced bipartite graph G satisfying that for every balanced set S, there is a bi-cycle of...

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...

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the spatial separation between neurons. In the continuum limit we derive that stable, balanced firing rate solutions require that the spatial spread of external in...

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...