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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 four regular graphs meeting this bound on the number of vertices are the 3-vertex 2-regular triangle , the 9-vertex 4-regular Paley graph, the 15-vertex 6-regular Kneser graph ,, and the 27-vertex 10-regular complement graph of the Schläfli graph.
It is designed so that "the graph of the normal distribution function is represented on it by a straight line", i.e. it can be used for a normal probability plot. [ 8 ] Polar coordinate paper has concentric circles divided into small arcs or 'pie wedges' to allow plotting in polar coordinates .
Table of graphs and parameters In the mathematical field of graph theory , a path graph (or linear graph ) is a graph whose vertices can be listed in the order v 1 , v 2 , ..., v n such that the edges are { v i , v i +1 } where i = 1, 2, ..., n − 1 .
Graph equations for line graphs and total graphs, DM Cvetkovic, SK Simic – Discrete Mathematics, 1975 Graph equations, graph inequalities and a fixed point theorem, DM Cvetkovic, IB Lackovic, SK Simic – Publ. Inst. Math.(Belgrade)., 1976 – elib.mi.sanu.ac.yu, PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE Nouvelle série, tome 20 (34), 1976,
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
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