We discuss two intrinsic weaknesses of the spectral graph partitioning method, both of which have practical consequences. The first is that spectral embeddings tend to hide the best cuts from the commonly used hyperplane rounding method. Rather than cleaning up the resulting suboptimal cuts with local search, we recommend the adoption of flow-based rounding. The second weakness is that for many...

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...

We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group A(T ) is defined by a signed graph T . Then we find a certain quotient G(T ) according to the graph T , which also have a natural map onto A(Dn). We prove that G(T ) is isomorphic to a semidirect product of a group K(m,n), with the Artin group A(Dn), where ...

BACKGROUND AND SCOPE Large networks, such as protein interaction networks, are extremely difficult to analyze as a whole. We developed Clust&See, a Cytoscape plugin dedicated to the identification, visualization and analysis of clusters extracted from such networks. IMPLEMENTATION AND PERFORMANCE Clust&See provides the ability to apply three different, recently developed graph clustering algo...

A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on sums powers integers weighted by Fermat quotients to next quotient power, namely third power quotient. Using this result Gessel identity (2005) combined with our past work (2021), we are able relate residues some truncated convolutions Bernoulli numbers full same kind. also establish con...

Consider the (p,q) simple connected graph . The sum absolute values of spectrum quotient matrix a make up graph's energy. objective this study is to examine energy identity graphs and zero-divisor commutative rings using group theory, applications. In study, derived from few classes ring R are examined.

We classify those manifolds mentioned in the title which have finite topological type. Namely we show that any such connected M is isomorphic to a hyperkähler quotient of a flat quaternionic vector space H by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n− 1 whose isometry group has rank n+ 1 is isometric to a 3-Sasakian quotient...

The exchange graph of a quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchange graph. Building on work of Iyama, Reiten, Thomas, and Todorov, we show that this directed graph is a semidistributive lattice by using the isomorphism to the lattice of functorially finite torsion cla...