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In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
quasi-line graph A quasi-line graph or locally co-bipartite graph is a graph in which the open neighborhood of every vertex can be partitioned into two cliques. These graphs are always claw-free and they include as a special case the line graphs. They are used in the structure theory of claw-free graphs. quasi-random graph sequence
graph minors, smaller graphs obtained from subgraphs by arbitrary edge contractions. The set of structures that are forbidden from belonging to a given graph family can also be called an obstruction set for that family. Forbidden graph characterizations may be used in algorithms for testing whether
Among other achievements, he introduced the use of linear algebraic methods to obtain graph drawings. Graph drawing also can be said to encompass problems that deal with the crossing number and its various generalizations. The crossing number of a graph is the minimum number of intersections between edges that a drawing of the graph in the ...
In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. [1] Formally, given a graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph.
This line attempts to display the non-random component of the association between the variables in a 2D scatter plot. Smoothing attempts to separate the non-random behaviour in the data from the random fluctuations, removing or reducing these fluctuations, and allows prediction of the response based value of the explanatory variable .
This is a list of graphical methods with a mathematical basis. Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization . There is also a list of computer graphics and descriptive geometry topics .
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...