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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).
Let V be a vector space of dimension n over a field F (with n≥2), and let Hom(V,V) denote the linear transformations on V.An n-trace diagram is a graph = (,), where the sets V i (i = 1, 2, n) are composed of vertices of degree i, together with the following additional structures:
In the mathematical field of graph theory, Fáry's theorem states that any simple, planar graph can be drawn without crossings so that its edges are straight line segments. That is, the ability to draw graph edges as curves instead of as straight line segments does not allow a larger class of graphs to be drawn.
One can also connect Kőnig's line coloring theorem to a different class of perfect graphs, the line graphs of bipartite graphs. If G is a graph, the line graph L(G) has a vertex for each edge of G, and an edge for each pair of adjacent edges in G. Thus, the chromatic number of L(G) equals the chromatic index of G.
The pioneering work of W. T. Tutte was very influential on the subject of graph drawing. 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 ...
Convex and strictly convex grid drawings of the same graph. In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.
Turn off the TV and phone. “All screens should be turned off at least one hour before bedtime,” says Dasgupta. “The blue light emitted by screens can interfere with melatonin production ...
Method and apparatus to draw line slices during calculation 5,740,345 Method and apparatus for displaying computer graphics data stored in a compressed format with an efficient color indexing system 5,657,435 Run slice line draw engine with non-linear scaling capabilities 5,627,957 Run slice line draw engine with enhanced processing capabilities