For improving the reliability and efficiency of the kineto-static analysis of complex robot systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, the vector bond graph model of universal joint are made. Based on this, the vector bond model of 3-RRRT parallel Manipulator is built. For solving the algebraic difficulties brought by differential ...

kProlog is a simple algebraic extension of Prolog with facts and rules annotated with semiring labels. We propose kProlog as a language for learning with kernels. kProlog allows to elegantly specify systems of algebraic expressions on databases. We propose some code examples of gradually increasing complexity, we give a declarative specification of some matrix operations and an algorithm to sol...

To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V . These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define...

Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit combinatorial description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise vertex disjoint e...

An irregular coloring of a graph is a proper vertex coloring that distinguishes vertices in the graph either by their own colors or by the colors of their neighbors. In algebraic graph theory, graphs with a certain amount of symmetry can sometimes be specified in terms of a group and a smaller graph called a voltage graph. In [3], Radcliffe and Zhang found a bound for the irregular chromatic nu...

In 1994, Cornuéjols and Novick published a classification of ideal and minimally non ideal circulant clutters. One of their main results for doing so relates contractions of these clutters, simple directed cycles in an appropriate graph, and algebraic conditions. The purpose of this paper is twofold: to correct a small inaccuracy of the necessity of the algebraic conditions in the original proo...

New lower bounds for eigenvalues of a simple graph are derived. Upper and lower bounds for eigenvalues of bipartite graphs are presented in terms of traces and degree of vertices. Finally a non-trivial lower bound for the algebraic connectivity of a connected graph is given.

An algebraic approach to graph theory can be useful in numerous ways. There is a relatively natural intersection between the fields of algebra and graph theory, specifically between group theory and graphs. Perhaps the most natural connection between group theory and graph theory lies in finding the automorphism group of a given graph. However, by studying the opposite connection, that is, find...

We prove that the algebraic connectivity a(G) of a graph embedded on a nonplanar surface satisfies a Heawood–type result. More precisely, it is shown that the algebraic connectivity of a surface S, defined as the supremum of a(G) over all graphs that can be embedded in S, is equal to the chromatic number of S. Furthermore, and with the possible exception of the Klein bottle, we prove that this ...