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Spectral graph theory. In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix . The adjacency matrix of a simple undirected graph is a real symmetric ...
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 .
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. [1] It is a generalization of the color refinement algorithm and has been first described by Weisfeiler and Leman in 1968. [2] The original formulation is based on graph canonization, a normal form for ...
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 ).
Topological graph theory. In mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. [1] It also studies immersions of graphs. Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for ...
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 ...
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 ...
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).