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A universal graph of this type was first constructed by Richard Rado [1] [2] and is now called the Rado graph or random graph. More recent work [3] [4] has focused on universal graphs for a graph family F: that is, an infinite graph belonging to F that contains all finite graphs in F. For instance, the Henson graphs are universal in this sense ...
In graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating vertex, as it forms a one-element dominating set in the graph. A graph that contains a universal vertex may be called a cone, and its universal vertex may be called the apex of the cone. [1]
For any connected graph G, it is possible to construct its universal covering graph. [3] This is an instance of the more general universal cover concept from topology; the topological requirement that a universal cover be simply connected translates in graph-theoretic terms to a requirement that it be acyclic and connected; that is, a tree .
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Sumner's conjecture (also called Sumner's universal tournament conjecture) is a conjecture in extremal graph theory on oriented trees in tournaments. It states that every orientation of every n {\displaystyle n} -vertex tree is a subgraph of every ( 2 n − 2 ) {\displaystyle (2n-2)} -vertex tournament. [ 1 ]
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can also be defined as the 1- skeleton of an ( n – 1 )-gonal pyramid .
The Rado graph, as numbered by Ackermann (1937) and Rado (1964).. In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge.