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The size of a graph is | | ... "Graph theory", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Graph theory tutorial Archived 2012-01-16 at the Wayback Machine;
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points ) and each of the related pairs of vertices is called an edge (also called link or line ...
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of a set for the set of vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs.
In graph theory, a tree is an ... The similar problem of counting all the subtrees regardless of size is #P-complete in the general case ... Discrete Mathematics, 88 ...
A universal graph is a graph that contains as subgraphs all graphs in a given family of graphs, or all graphs of a given size or order within a given family of graphs. 2. A universal vertex (also called an apex or dominating vertex) is a vertex that is adjacent to every other vertex in the graph.
If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t belongs to the set T. In an unweighted undirected graph, the size or weight of a cut is the number of edges crossing the cut. In a weighted graph, the value or weight is defined by the sum of the weights of the edges crossing the ...
Equivalently, each edge in the graph has at most one endpoint in . A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening. [1]
Star graphs with m equal to 1 or 2 need only dimension 1. The dimension of a complete bipartite graph K m , 2 {\displaystyle K_{m,2}} , for m ≥ 3 {\displaystyle m\geq 3} , can be drawn as in the figure to the right, by placing m vertices on a circle whose radius is less than a unit, and the other two vertices one each side of the plane of the ...