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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.
The order of a graph is | |, its number of vertices. The size of a graph is | |, its number of edges. The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices.
The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node.
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 order of a bramble is the smallest size of a set of vertices that has a nonempty intersection with all of the subgraphs. The treewidth of a graph is the maximum order of any of its brambles. branch A path of degree-two vertices, ending at vertices whose degree is unequal to two. [7] branch-decomposition
The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...
Graph (discrete mathematics), a structure made of vertices and edges Graph theory, the study of such graphs and their properties; Graph (topology), a topological space resembling a graph in the sense of discrete mathematics; Graph of a function; Graph of a relation; Graph paper; Chart, a means of representing data (also called a graph)
Certain kinds of graphs may be characterized by the order dimensions of their incidence posets: a graph is a path graph if and only if the order dimension of its incidence poset is at most two, and according to Schnyder's theorem it is a planar graph if and only if the order dimension of its incidence poset is at most three (Schnyder 1989).