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Pages in category "Unsolved problems in graph theory" The following 32 pages are in this category, out of 32 total. This list may not reflect recent changes. A.
The Hosoya index of a graph G, its number of matchings, is used in chemoinformatics as a structural descriptor of a molecular graph. It may be evaluated as m G (1) ( Gutman 1991 ). The third type of matching polynomial was introduced by Farrell (1980) as a version of the "acyclic polynomial" used in chemistry .
In mathematics and computer science, 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 ).
This is a list of graph theory topics, by Wikipedia page. See glossary of graph theory for basic terminology. Examples and types of graphs. Amalgamation;
The discharging method is used to prove that every graph in a certain class contains some subgraph from a specified list. The presence of the desired subgraph is then often used to prove a coloring result. [1] Most commonly, discharging is applied to planar graphs. Initially, a charge is assigned to each face and each vertex of the graph. The ...
More formally, a graph property is a mapping from the class of all graphs to {,} such that isomorphic graphs are mapped to the same value. For example, the property of containing at least one vertex of degree two is a graph property, but the property that the first vertex has degree two is not, because it depends on the labeling of the graph ...
Star graphs with m equal to 1 or 2 need only dimension 1. The dimension of a complete bipartite graph K m , 2 {\displaystyle K_{m,2}} , for m ≥ 3 {\displaystyle m\geq 3} , can be drawn as in the figure to the right, by placing m vertices on a circle whose radius is less than a unit, and the other two vertices one each side of the plane of the ...
A vertex in a directed graph whose second neighborhood is at least as large as its first neighborhood is called a Seymour vertex. [5]In the second neighborhood conjecture, the condition that the graph have no two-edge cycles is necessary, for in graphs that have such cycles (for instance the complete oriented graph) all second neighborhoods may be empty or small.