Graceful numbers.
Graceful signed graphs
A -sigraph is an ordered pair where is a -graph and is a function which assigns to each edge of a positive or a negative sign. Let the sets and consist of positive and negative edges of , respectively, where . Given positive integers and , is said to be -graceful if the vertices of can be labeled with distinct integers from the set such that when each edge of is assigned the product of its sign and the absolute difference of the integers assigned to and the...
Graceful signed graphs: II. The case of signed cycles with connected negative sections
In our earlier paper [9], generalizing the well known notion of graceful graphs, a -signed graph of order , with positive edges and negative edges, is called graceful if there exists an injective function that assigns to its vertices integers such that when to each edge of one assigns the absolute difference the set of integers received by the positive edges of is and the set of integers received by the negative edges of is . Considering the conjecture therein that all...
Graceful tree conjecture for infinite trees.
Grad und lokaler Zusammenhang in endlichen Graphen.
Gradual partition of a graph into complete graphs
Graph centers used for stabilization of matrix factorizations
Systems of consistent linear equations with symmetric positive semidefinite matrices arise naturally while solving many scientific and engineering problems. In case of a "floating" static structure, the boundary conditions are not sufficient to prevent its rigid body motions. Traditional solvers based on Cholesky decomposition can be adapted to these systems by recognition of zero rows or columns and also by setting up a well conditioned regular submatrix of the problem that...
Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories
The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.
Graph color extensions: When Hadwiger's conjecture and embeddings help.
Graph coloring problems with applications in algebraic logic
Graph colorings with local constraints - a survey
We survey the literature on those variants of the chromatic number problem where not only a proper coloring has to be found (i.e., adjacent vertices must not receive the same color) but some further local restrictions are imposed on the color assignment. Mostly, the list colorings and the precoloring extensions are considered. In one of the most general formulations, a graph G = (V,E), sets L(v) of admissible colors, and natural numbers for the vertices v ∈ V are given, and the question is whether...
Graph compositions. I: Basic enumeration.
Graph connectivity and Wiener index
Graph cycles and diagram commutativity
Graph domination in distance two
Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that holds for = all connected graphs without induced (u ≥ 2). (In particular, ₂ = K₁ and...
Graph drawing by high-dimensional embedding.
Graph equations for line graphs and n-th distance graphs.
Graph Equations For Line Graphs And The N-Th Power Graphs I
Graph equations, graph inequalities and a fixed point theorem.
Graph factorization, general triple systems, and cyclic triple systems.