In this paper we propose a criteria to establish the integrability of N = 2 super-symmetric massive theories. The basic data required are the vacua and the spectrum of Bogomolnyi solitons, which can be neatly encoded in a graph (nodes=vacua and links= Bogomolnyi solitons). Integrability is then equivalent to the existence of solutions of a generalized Yang-Baxter equation which is built up from...

We present HOMER, an analysis and visualization tool for ontology alignment. HOMER features a radial-graph display GUI, a complete execution trace that allows the user to override and navigate to any match decisions during at runtime and a comparison mode that displays multiple alignments in parallel. HOMER contains a builtin plugin for the ILIADS ontology alignment algorithm, but other algorit...

We present AGNES – a novel algorithm for presenting diversified graphical entity summarisations on semantic knowledge graphs. The main idea is to compute the positions of the vertices in radial system of coordinates based on recursive, in-order traversal of the BST spanning tree of the graph. The implementation of the algorithm is compared on real data with other, existing visualisation tools. ...

We address the problem of unsupervised learning on graphs. The contribution is twofold: (1) we propose an EM algorithm for estimating the parameters of a mixture of radial densities on graphs on the basis of the graph orbifold framework; and (2) we compare orbifold-based clustering algorithms including the proposed EM algorithm against stateof-the-art methods based on pairwise dissimilarities. ...

We consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, count the vertices on coordination shells of a vertex, defined via the graph distance given by the tiling. For the Ammann-Beenker tiling, we find that coordination shells consist of complete shelling orbits, which enabl...

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the annihilating-ideal graph of a commutative ring $r$ is denoted by $ag(r)$, whose vertices are all nonzero ideals of $r$ with nonzero annihilators and two distinct vertices $i$ and $j$ are adjacent if and only if $ij=0$. in this article, we completely characterize rings $r$ when $gr(ag(r))neq 3$.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.