A lot of real-life data are of graph nature. However, it is not until recently that business begins to exploit data’s connectedness for business insights. On the other hand, RDBMSs are a mature technology for data management, but they are not for graph processing. Take graph traversal, a common graph operation for example, it heavily relies on a graph primitive that accesses a given node’s neig...

In this paper, we present a modelling operation dedicated to animation. This operation, called thickening, is a generalization of the extrusion operation. It allows to build from a graph 3-D objects with circular section and 4-D objects with spherical or toric section. Moreover, the date and the number of mergings and splittings in the associated animation are perfectly controlled, and the traj...

Let ω(G) and χ(G) be the clique number and the chromatic number of a graph G. Mycielski [11] presented a construction that for any n creates a graph Mn which is triangle-free (ω(G) = 2) with χ(G) > n. The starting point is the complete graph of two vertices (K2). M(n+1) is obtained from Mn through the operation μ(G) called the Mycielskian of a graph G. We first define the operation μ(G) and the...

Rainbow vertex-connection number is the minimum colors assignment to vertices of graph, such that each vertex connected by a path whose edges have distinct and denoted . The rainbow connection can be applied graphs resulting from operations. One methods create new graph perform operations between two graphs. Thus, this research uses comb product operation determine rainbow-vertex cycle complete...

In this paper, we introduce the splicing operation on graph P system with the feature of conditional communication. We use the notions of Fruend graph splicing and generate the string graph languages. We study the generative power of the splicing graph P system with conditional communication with the other classes of string graph languages and give comparison results of the languages generated ...

Edge-colorings are used to extend the notion of the graph Cartesian product to a quotient operation that allows for the formation of graph fractions. Fractional graphs form a group that is isomorphic to the positive rational numbers.

We define graph representations modulo integers and prove that any finite graph has a representation modulo some integer. We use this to obtain a new, simpler proof of Lindner, E. Mendelsohn, N. Mendelsohn, and Wolk’s result that any finite graph can be represented as an orthogonal latin square graph. Let G be a graph with vertices v,, . . . , u, and let n be a natural number. We say that G is ...

In the design activity, part geometry is assembled together to create an assembly model. The number of parts can range from a few tens to a few millions and typically the relationships among them construct a closed-loop with under-constrained states in a constraint graph. In this paper, we propose an efficient and robust 3D constraint solving method for determining part positions in closed-loop...

Partitioning is a fundamental operation on graphs. In this paper we briefly review the basic concepts of graph partitioning and its relationship to digital mesh processing. We also elaborate on the connection between graph partitioning and spectral graph theory. Applications in computer graphics are described.