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Plotting sin(x) with pst-plot. PSTricks commands are low level, so many LaTeX packages have been made in order to ease the creation of several kinds of graphics that are commonly used on mathematical typesetting. pst-plot provides commands for creating function graphs. Consider the following example:
The lexicographic product of graphs. In graph theory, the lexicographic product or (graph) composition G ∙ H of graphs G and H is a graph such that the vertex set of G ∙ H is the cartesian product V(G) × V(H); and; any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent to x in G or u = x and v is ...
This allows the two congruent purple-outline triangles and to be constructed, each with hypotenuse and angle at their base. The sum of the heights of the red and blue triangles is sin θ + sin φ {\displaystyle \sin \theta +\sin \varphi } , and this is equal to twice the height of one purple triangle, i.e. 2 sin p cos q ...
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set S {\displaystyle S} of vertices such that for every two vertices in S {\displaystyle S} , there is no edge connecting the two.
In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Földes and Hammer ( 1977a , 1977b ), and independently introduced by Tyshkevich and Chernyak ( 1979 ), where they called these graphs "polar graphs" ( Russian ...
The strong product of any two graphs can be constructed as the union of two other products of the same two graphs, the Cartesian product of graphs and the tensor product of graphs. An example of a strong product is the king's graph, the graph of moves of a chess king on a chessboard, which can be constructed as a strong product of path graphs ...
The graph of a function on its own does not determine the codomain. It is common [3] to use both terms function and graph of a function since even if considered the same object, they indicate viewing it from a different perspective. Graph of the function () = over the interval [−2,+3]. Also shown are the two real roots and the local minimum ...
The derivative of the sum is thus equal to the sum multiplied by sec θ. This enables multiplying sec θ by sec θ + tan θ in the numerator and denominator and performing the following substitutions: