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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 ).
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.
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants .
Total graph. Tree (graph theory). Trellis (graph) Turán graph. Ultrahomogeneous graph. Vertex-transitive graph. Visibility graph. Museum guard problem. Wheel graph.
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 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 ...
Edge-graceful labeling. In graph theory, an edge-graceful labeling is a type of graph labeling for simple, connected graphs in which no two distinct edges connect the same two distinct vertices and no edge connects a vertex to itself. Edge-graceful labelings were first introduced by Sheng-Ping Lo in his seminal paper.
Network science. In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.