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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 ).
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.
The Petersen graph is an undirected graph with ten vertices and fifteen edges, commonly drawn as a pentagram within a pentagon, with corresponding vertices attached to each other. It has many unusual mathematical properties, and has frequently been used as a counterexample to conjectures in graph theory. [1] [2] The book uses these properties ...
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 ...
In order to do so, it covers several other significant topics in graph theory, number theory, and group theory. It was written by Giuliana Davidoff, Peter Sarnak, and Alain Valette, and published in 2003 by the Cambridge University Press, as volume 55 of the London Mathematical Society Student Texts book series.
Path (graph theory) A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
The Turán graph T(n,r) is an example of an extremal graph. It has the maximum possible number of edges for a graph on n vertices without (r + 1)-cliques. This is T(13,4). Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence ...