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2. Logic of graphs - Wikipedia

   en.wikipedia.org/wiki/Logic_of_graphs

   The remaining blue vertices form the 2-core of the graph. Least fixed point based logics of graphs extend the first-order logic of graphs by allowing predicates (properties of vertices or tuples of vertices) defined by special fixed-point operators. This kind of definition begins with an implication, a formula stating that when certain values ...

3. Syntax diagram - Wikipedia

   en.wikipedia.org/wiki/Syntax_diagram

   Syntax diagram. Syntax diagrams (or railroad diagrams) are a way to represent a context-free grammar. They represent a graphical alternative to Backus–Naur form, EBNF, Augmented Backus–Naur form, and other text-based grammars as metalanguages. Early books using syntax diagrams include the "Pascal User Manual" written by Niklaus Wirth [1 ...

4. Cartesian product - Wikipedia

   en.wikipedia.org/wiki/Cartesian_product

   The Cartesian square of a set X is the Cartesian product X2 = X × X. An example is the 2-dimensional plane R2 = R × R where R is the set of real numbers: [1] R2 is the set of all points (x,y) where x and y are real numbers (see the Cartesian coordinate system). The n-ary Cartesian power of a set X, denoted.

5. Vizing's theorem - Wikipedia

   en.wikipedia.org/wiki/Vizing's_theorem

   In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree Δ of the graph. At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ colors suffice, and ...

6. Graph (discrete mathematics) - Wikipedia

   en.wikipedia.org/wiki/Graph_(discrete_mathematics)

   A cycle graph or circular graph of order n ≥ 3 is a graph in which the vertices can be listed in an order v 1, v 2, …, v n such that the edges are the {v i, v i+1} where i = 1, 2, …, n − 1, plus the edge {v n, v 1}. Cycle graphs can be characterized as connected graphs in which the degree of all vertices is 2. If a cycle graph occurs as ...

7. Directed acyclic graph - Wikipedia

   en.wikipedia.org/wiki/Directed_acyclic_graph

   Directed acyclic graph. In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop ...

8. Existential graph - Wikipedia

   en.wikipedia.org/wiki/Existential_graph

   An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, [1] and continued to develop the method until his death in 1914. They include both a separate graphical notation for logical statements and a logical calculus, a formal ...

9. Robertson–Seymour theorem - Wikipedia

   en.wikipedia.org/wiki/Robertson–Seymour_theorem

   A minor of an undirected graph G is any graph that may be obtained from G by a sequence of zero or more contractions of edges of G and deletions of edges and vertices of G.The minor relationship forms a partial order on the set of all distinct finite undirected graphs, as it obeys the three axioms of partial orders: it is reflexive (every graph is a minor of itself), transitive (a minor of a ...