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Grundy number. An optimal greedy coloring (left) and Grundy coloring (right) of a crown graph. The numbers indicate the order in which the greedy algorithm colors the vertices. In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring strategy that ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines ).
Graph isomorphism. In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H. such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism ...
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [ 3]: ND22, ND23. Vehicle routing problem.
Graph. Worst-case performance. Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm.
Degree (graph theory) In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. [1] The degree of a vertex is denoted or . The maximum degree of a graph is denoted by , and is the maximum of 's ...
v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [ 1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently ...