In mathematical logic and graph theory, an implication graph is a skew-symmetric, directed graph G = (V, E) composed of vertex set V and directed edge...

type of directed graph, the implication graph, which expresses the variables of an instance and their negations as vertices in a graph, and constraints...

other Implication table, a tool used to facilitate the minimization of states in a state machine Implication graph, a skew-symmetric directed graph used...

finding a maximum independent set of a graph. Every maximum independent set also is maximal, but the converse implication does not necessarily hold. A set is...

resulting graph is called an implication graph. Arbitrarily pick another branching variable, x3. Apply unit propagation and find the new implication graph. Here...

In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly...

the implication graphs used to efficiently solve the 2-satisfiability problem. As defined, e.g., by Goldberg & Karzanov (1996), a skew-symmetric graph G...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

Graph neural networks (GNN) are specialized artificial neural networks that are designed for tasks whose inputs are graphs. One prominent example is molecular...

knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used...

implication) is a binary operation commonly used in logic. When the conditional symbol → {\displaystyle \to } is interpreted as material implication,...

green clauses becomes True After making several decisions, we find an implication graph that leads to a conflict. Now backtrack to immediate level and by...

hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two...

converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q...

the implication graph are dependent. but thanks to the semi-final selection phase, we can prove that the probability that the implication graph contains...

knowledge elements can be structured and interrelated (as a tree, graph, tree plus graph, spatially, categorically, as n-ary links, chronologically, or ZigZag);...

that a graph sampled from G(n, M) has property P tends to a as n → ∞. Then the probability that G(n, p) has property P also tends to a. Implications in the...

inference tools, the graphs enable researchers to estimate effect sizes from non-experimental data, derive testable implications of the assumptions encoded...

taking the converse of an implication in logic. The name transpose is because the adjacency matrix of the transpose directed graph is the transpose of the...

time, by an algorithm involving strong connectivity analysis of its implication graph. The 2-satisfiability problem is a special case of TQBF for these...

equivalent for a bipartite graph G = (X+Y, E): G admits an X-perfect matching. G admits an X-perfect fractional matching. The implication follows directly from...

social graph is a graph that represents social relations between entities. It is a model or representation of a social network. The social graph has been...

the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences...

Hockey stick graphs present the global or hemispherical mean temperature record of the past 500 to 2000 years as shown by quantitative climate reconstructions...

its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To...

graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor...

symmetries of an infinite graph; alternatively, the axiom of regularity eliminates the need for choice. Furthermore, this implication is strict, as there are...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

pairwise edge-disjoint paths from x to y. The implication for the graph G is the following version: A graph is k-edge-connected (it remains connected after...

frequent retraining. GraphRAG (coined by Microsoft Research) is a technique that extends RAG with the use of a knowledge graph (usually, LLM-generated)...