Search results
Results From The WOW.Com Content Network
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
Order theory is a branch of mathematics that ... is bottom and top or zero ... to the edges of a graph. In this way, each order is seen to be ...
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 ...
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)
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.
2. Topological graph theory is the study of graph embeddings. 3. Topological sorting is the algorithmic problem of arranging a directed acyclic graph into a topological order, a vertex sequence such that each edge goes from an earlier vertex to a later vertex in the sequence. totally disconnected Synonym for edgeless. tour
One can define the adjacency matrix of a directed graph either such that a non-zero element A ij indicates an edge from i to j or; it indicates an edge from j to i. The former definition is commonly used in graph theory and social network analysis (e.g., sociology, political science, economics, psychology). [5]
Because of the order of zeros and poles being defined as a non-negative number n and the symmetry between them, it is often useful to consider a pole of order n as a zero of order –n and a zero of order n as a pole of order –n. In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0.