Search results
Results from the WOW.Com Content Network
The Rado graph, an infinite graph that models exactly the first-order sentences that are almost always true of finite graphs. Glebskiĭ et al. (1969) and, independently, Fagin (1976) proved a zero–one law for first-order graph logic; Fagin's proof used the compactness theorem.
As elsewhere in graph theory, the order-zero graph (graph with no vertices) is generally not considered to be a tree: while it is vacuously connected as a graph (any two vertices can be connected by a path), it is not 0-connected (or even (−1)-connected) in algebraic topology, unlike non-empty trees, and violates the "one more vertex than ...
This is not a first-order axiomatization as one of Hilbert's axioms is a second order completeness axiom. Tarski's axioms are a first-order axiomatization of Euclidean geometry. Tarski showed this axiom system is complete and decidable by relating it to the complete and decidable theory of real closed fields.
A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed.
Graph order, the number of nodes in a graph; First order and second order logic of graphs; Topological ordering of directed acyclic graphs; Degeneracy ordering of undirected graphs; Elimination ordering of chordal graphs; Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)
first order The first order logic of graphs is a form of logic in which variables represent vertices of a graph, and there exists a binary predicate to test whether two vertices are adjacent. To be distinguished from second order logic, in which variables can also represent sets of vertices or edges.-flap
The order of a graph is ... of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory. ... number is zero by definition ...
The order-zero graph, K 0, is the unique graph having no vertices (hence its order is zero). It follows that K 0 also has no edges. Thus the null graph is a regular graph of degree zero. Some authors exclude K 0 from consideration as a graph (either by definition