The first step in the analysis of a structure is to generate its configuration. Different means are available for this purpose. The use of graph products is an example of such tools. In this paper, the use of product graphs is extended for the formation of different types of structural models. Here weighted graphs are used as the generators and the connectivity properties of different models ar...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

Many geometric constraint solvers use a combinatorial or graph algorithm to generate a decompositionrecombination (DR) plan. A DR plan recursively decomposes the system of polynomial equations into small, generically rigid subsystems that are more likely to be successfully solved by algebraic-numeric solvers. In this paper we show that, especially for 3D geometric constraint systems, a further ...

The algebraic graph transformation approach was initiated in 1973 and supports the rule-based modification of graphs based on pushout constructions. The vertex and edge types used within the rules (or productions) as well as possible inheritance relationships defined between them are specified in the type graph. However, the termination proof can only be accomplished for graph transformation sy...

This paper is an attempt to investigate the possibilities to link algebraic fuzzy set theory with the theory of word graphs. In both theories concepts are studied and concepts can be set in correspondence. This enables to use algebraic results in the context of word graph theory.

Today, we will use an algebraic approach to solve the matching problem. Our goal is to derive an algebraic test for deciding if a graph G = (V, E) has a perfect matching. We may assume that the number of vertices is even since this is a necessary condition for having a perfect matching. First, we will define a few basic needed notations.

In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number Fn+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pe...

The algebraic Kekulé structure of a finite catacondensed benzenoid graph with h hexagons is described by a binary code of length h. The procedure can be reversed, any (algebraic) Kekulé structure can be recovered from its binary code. c © 2007 Elsevier Ltd. All rights reserved.

An algorithm is presented for the geometric analysis of an algebraic curve f (x,y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the plane, augmented with adjacency information. The adjacency information describes the curve’s topology by a topologically equivalent planar graph. The numerical data in the CAD gives an embedding