This paper presents a new approach to fractal image generation by translating the evolution of graph grammar into graphics output. It uses the algebraic approach of graph grammar as a powerful abstract modeling tool for the generation of selfsimilar fractal images via its graph production, derivations and double-pushout construction. We focus on three proposed methods for image generation which...

Counting the number of imbeddings in various surfaces of each of the graphs in an interesting family is an ongoing topic in topological graph theory. Our special focus here is on a family of closed chains of copies of a given graph. We derive double-root partials for open chains of copies of a given graph, and we then apply a self-amalgamation theorem, thereby obtaining genus distributions for ...

The development of a denotational framework for graph transformation systems proved elusive so far. Despite the existence of many formalisms for modelling various notions of rewriting, the lack of an explicit, algebraic notion of “term” for describing a graph (thus different from the usual view of a graph as an algebra in itself) frustrated the efforts of the researchers. Resorting to the theor...

In this paper we introduce a new class of double coset Cayley digraphs induced by quasigroups. These graphs can be considered as the generalization of Double Coset Cayley Digraphs induced by loops. Moreover, various graph properties are expressed in terms of algebraic properties. This did not attract much attention in the literature.

A set S of vertices in a graph G is a double total dominating set, abbreviated DTDS, of G if every vertex of G is adjacent to least two vertices in S. The minimum cardinality of a DTDS of G is the double total domination number of G. In this paper, we study the DTDS of the generalized Petersen graphs. Mathematics Subject Classification: 05C35

An orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipartite graph Kmn,mn (for any values ofm,n) and all graphs in the collection are isomorphic to certa...

Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system. We now introduce the notion of modules over an A2-planar algebra, and describe certain irreducible Hilbert A2-TL-modules. We construct an A2-graph planar algeb...

This paper gives a truly concurrent semantics with sharing of resources for the K semantic framework, an executable (term-)rewritingbased formalism for defining programming languages and calculi. Akin to graph rewriting rules, the K (rewrite) rules explicitly state what can be concurrently shared with other rules. The desired true concurrency is obtained by translating the K rules into a novel ...

Abstract. Given any simple biorientable graph it is shown that there exists a weak *-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum decomposition of the space of paths into orthogonal subspaces one of which is the space of essential paths. Two simple examples are worked out with certain detail, the...

The celebrated grid exclusion theorem states that for every h-vertex planar graph H , there is a constant ch such that if a graph G does not contain H as a minor then G has treewidth at most ch. We are looking for patterns of H where this bound can become a low degree polynomial. We provide such bounds for the following parameterized graphs: the wheel (ch = O(h)), the double wheel (ch = O(h 2 ·...