We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the relations in UML interaction diagrams. Then, we provide a set of algebraic graph rewrite rules tha...

The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, k-colorability of a graph can be characterized in terms of whether its graph polynomial is contained in a certain ideal. In this paper, we interpret unique colorability in an analogous manner and prove an algebraic characterization for uniquely k-colo...

We consider extremal problems for algebraic graphs, that is, graphs whose vertices correspond to vectors in Rd, where two vectors are connected by an edge according to an algebraic condition. We also derive a lower bound on the rank of the adjacency matrix of a general abstract graph using the number of 4-cycles and a parameter which measures how close the graph is to being regular. From this w...

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, bu...

Graph eigenvalues are examples of totally real algebraic integers, i.e. roots of real-rooted monic polynomials with integer coefficients. Conversely, the fact that every totally real algebraic integer occurs as an eigenvalue of some finite graph is a deep result, conjectured forty years ago by Hoffman, and proved seventeen years later by Estes. This short paper provides an independent and eleme...

Relational algebra in the sense of Schr oder and Tarski has been thoroughly studied by mathematicians from the universal algebraic viewpoint and some research has shown many applications of the relational calculus in the elds of graph theory and computer science This paper addresses the eld of process algebraic languages which are used for the speci cation and veri cation of communicating syste...

Measuring the connectivity strength between a pair of vertices in a graph is one of the most vital concerns in numerous computational graph problems. In this paper we propose a local measure, together with an efficient algorithm that is scalable and parallelizable. In the heart of the algorithm is an iterative process that propagates and refines random values associated with each vertex. The co...

This thesis concerns exact and inexact graph matching algorithms based on algebraic representsations of graphs, i.e., matrices or vectors. We focus on approximate graph matching with the use of descriptors, understood as pattern vectors associated to graphs. Several graph descriptors are presented, including ones known in literature and new ones created on the basis of various vertex-gathered i...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...