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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.
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 ...
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 ).
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 .
Neighbourhood (graph theory) In this graph, the vertices adjacent to 5 are 1, 2 and 4. The neighbourhood of 5 is the graph consisting of the vertices 1, 2, 4 and the edge connecting 1 and 2. In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is ...
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.
The problem of constructing a solution for the graph realization problem with the additional constraint that each such solution comes with the same probability was shown to have a polynomial-time approximation scheme for the degree sequences of regular graphs by Cooper, Martin, and Greenhill. The general problem is still unsolved. References
Decomposition of the complete graph into three copies of +, solving the Oberwolfach problem for the input (,). The Oberwolfach problem is an unsolved problem in mathematics that may be formulated either as a problem of scheduling seating assignments for diners, or more abstractly as a problem in graph theory, on the edge cycle covers of complete graphs.
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