The initial phase of the inspiral process a binary black-hole system can be described by perturbation theory. At third post-Minkowskian order two-loop double box graph, known as H-graph, contributes. In this talk we report how all master integrals H-graph with equal masses expressed up to weight four in terms multiple polylogarithms. We also discuss techniques for unequal mass case. essential c...

Hierarchically distributed graph transformation ooers means to model diierent aspects of open distributed systems very intuitively in a graphical way. The distribution topology as well as local object structures are represented graphically. Distributed actions such as local actions, network activities, communication and synchronization can be described homogeneously using the same method: graph...

The motive associated to the second Symanzik polynomial of double-box two-loop Feynman graph with generic masses and momenta is shown be an elliptic curve.

The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a G, in which no two vertices are incident to edges colored with same set colors. an G called edge-chromatic index. In this paper, I compute index Anti-prism, sunflower graph, double triangular winged prism, rectangular prism and Polygonal snake graph.

Let G be a graph with p vertices and q edges. A total neighborhood prime labeling of is in which the edges are assigned labels from 1 to + such that gcd each non degree vertex equal 1. admits called graph. In this paper, we examine trees as (n, k, m) double star trees, spiders, caterpillars firecrackers.

Abstract Graphical notations are already popular for the design of software, as witnessed by the success of the Uniform Modeling Languages (UML). In this paper, we advocate the use of graphs and graph transformation for programming graph-based systems. Our case study, the flattening of hierarchical statecharts, reveals that cloning, a recently proposed transformation concept, makes graph transf...

Fleischner [3] has proposed a novel approach to several deep graph-theoretic conjectures, such as the Cycle Double Cover Conjecture [9,10] or the 5-Flow Conjecture of Tutte [12]. A key ingredient in this approach is the Bipartizing Matchings Conjecture (Conjecture 1.2 below, abbreviated BM Conjecture). In this paper, we introduce the notion of an Eulerian coloring of a trigraph, providing a set...

Given a bipartite graph G(U ∪ V, E) with n vertices on each side, an independent set I ∈ G such that |U ⋂ I| = |V ⋂ I| is called a balanced bipartite independent set. A balanced coloring of G is a coloring of the vertices of G such that each color class induces a balanced bipartite independent set in G. If graph G has a balanced coloring we call it colorable. The coloring number χB(G) is the mi...

We continue here the development of our description of the pullback approach to graph rewriting-already shown to encompass both the NCE and the double-pushout approach, by describing parallel application of rewriting rules. We show that this new framework provides a genuine deenition of parallel rewriting (parallel application of several rewriting rules at several diierent places in the graph i...

The Small Cycle Double Cover Conjectnre, due to J .A. Bondy, states that every simple bridgeless graph on n vertices has a cycle double cover with at most (n 1) cycles. There are a number of classes of graphs for which this conjecture is known to hold; for example, triangulations of surfaces, complete graphs, and 4-connected planar graphs. In this article, we prove that the conjecture holds for...