Let G be a connected graph and let L(G) be its Laplacian matrix. We show that given a graph G with a point of articulation u, and a spanning tree T , there is a way to give weights to the edges of G, so that u is the characteristic vertex and the monotonicity property holds on T . A restricted graph is a graph with a restriction that each block can have at most two points of articulation. We su...

The conception of an ontology is a complex task influenced by numerous factors like the point of view of the authors or the level of details. Consequently, several ontologies have been developed to model identical or related domains leading to partially overlapping representations. This divergence of conceptualization requires the study of ontologies merging in order to create a common reposito...

One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the maximization of a quality function called modularity, which in turn is based upon particular quadratic forms associated to a real symmetric modularity matrix M , defined in terms of the adjacency matrix and a rank one null m...

My research uses algebraic and geometric methods to prove theorems in extremal combinatorics. Going the other way, I also use combinatorial methods to prove algebraic results. Algebraic methods are deeply embedded in my work and nearly all of my success in graph theoretic research has come from attacking purely combinatorial problems through the lens of algebra, combinatorial number theory, or ...

The language of sketches is as concise and powerful as higher order logic and as handy as conventional ER-diagrams. We discuss its beneets in respect to problems of schema integration. It is evident that a chief property of the next generation information systems is their organization on cooperative principles. Typically, applications involved in a cooperative system have to access data stored ...

We show how graph rewriting can be described with a single pushout in a suitable category of graphs, and compare our result with the conventional approach which uses double pushouts.

The single-pushout approach to graph transformation interprets a double-pushout transformation rule of the classical algebraic approach which consists of two rotul graph morphisms as a single particll morphism from the left-to the right-hand side. The notion of a double-pushout diagram for the transformation process can then be substituted by a single-pushout diagram in an appropriate category ...

Let A(G) denote the adjacency matrix of the graph G. The polynomial pA(G)(x) is usually referred to as the characteristic polynomial of G. For convenience, we use p(G, x) to denote pA(G)(x). The spectrum of a graph G is the set of eigenvalues of A(G) together with their multiplicities. Since A (short for A(G)) is a real symmetric matrix, basic linear algebra tells us a few thing about A and its...