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Total graph. Tree (graph theory). Trellis (graph) Turán graph. Ultrahomogeneous graph. Vertex-transitive graph. Visibility graph. Museum guard problem. Wheel 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 ). A distinction is made between undirected graphs, where edges link ...
The vehicle routing problem ( VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John ...
Linear forest. In graph theory, a branch of mathematics, a linear forest is a kind of forest where each component is a path graph, [1] : 200 or a disjoint union of nontrivial paths. [2] : 246 Equivalently, it is an a cyclic and claw-free graph. [3] : 130, 131 An acyclic graph where every vertex has degree 0, 1, or 2 is a linear forest.
Digraph realization problem. The digraph realization problem is a decision problem in graph theory. Given pairs of nonnegative integers , the problem asks whether there is a labeled simple directed graph such that each vertex has indegree and outdegree .
Closure problem. In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is the task of finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph. [1] [2] It may be solved in polynomial time using a reduction to the ...
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 ...
Vizing's theorem. In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree Δ of the graph. At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ ...