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K 4 as the half-square of a cube graph. The half-square of a bipartite graph G is the subgraph of G 2 induced by one side of the bipartition of G. Map graphs are the half-squares of planar graphs, [18] and halved cube graphs are the half-squares of hypercube graphs. [19] Leaf powers are the subgraphs of powers of trees induced by the leaves of ...
A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines). A distinction is made between undirected graphs , where edges link two vertices symmetrically, and directed graphs , where edges link two vertices asymmetrically.
The graph of the square function y = x 2 is a parabola. The squaring operation defines a real function called the square function or the squaring function. Its domain is the whole real line, and its image is the set of nonnegative real numbers. The square function preserves the order of positive numbers: larger numbers have larger squares.
5. A chord of a circle is a line segment connecting two points on the circle; the intersection graph of a collection of chords is called a circle graph. chromatic Having to do with coloring; see color. Chromatic graph theory is the theory of graph coloring. The chromatic number χ(G) is the minimum number of colors needed in a proper coloring of G.
A 2-vertex-connected graph, its square, and a Hamiltonian cycle in the square. In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that, if is a 2-vertex-connected graph, then the square of is Hamiltonian.
The characterization of squaregraphs in terms of distance from a root and links of vertices can be used together with breadth first search as part of a linear time algorithm for testing whether a given graph is a squaregraph, without any need to use the more complex linear-time algorithms for planarity testing of arbitrary graphs.
The expression b 2 = b · b is called "the square of b" or "b squared", because the area of a square with side-length b is b 2. (It is true that it could also be called "b to the second power", but "the square of b" and "b squared" are more traditional)
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.