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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).
The papers in a composition book often have the baseline and cap line printed in blue to aid writing, with a (sometimes red) vertical line for a margin on the left hand of every page. Traditionally, the inside back cover contains a table of the weights and measures of the English ( imperial ) system printed for reference; however, this feature ...
The verb and its object, when present, are separated by a line that ends at the baseline. If the object is a direct object, the line is vertical. If the object is a predicate noun or adjective, the line looks like a backslash, \, sloping toward the subject. Modifiers of the subject, predicate, or object are placed below the baseline:
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
5 Graph limits. 6 Graphs in logic. 7 Mazes and labyrinths. 8 Algorithms. 9 Other topics. 10 Networks, network theory. 11 Hypergraphs. ... Intersection (Line) Graphs ...
The graph of the 3-3 duoprism (the line graph of ,) is perfect.Here it is colored with three colors, with one of its 3-vertex maximum cliques highlighted. In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph.
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
Planar graphs: K 5 and K 3,3: Homeomorphic subgraph Kuratowski's theorem: K 5 and K 3,3: Graph minor Wagner's theorem: Outerplanar graphs: K 4 and K 2,3: Graph minor Diestel (2000), [1] p. 107: Outer 1-planar graphs: Six forbidden minors Graph minor Auer et al. (2013) [2] Graphs of fixed genus: A finite obstruction set Graph minor Diestel (2000 ...