Directed graphIn mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. In formal terms, a directed graph is an ordered pair where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.
Directed acyclic graphIn mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions.
Main-group elementIn chemistry and atomic physics, the main group is the group of elements (sometimes called the representative elements) whose lightest members are represented by helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, and fluorine as arranged in the periodic table of the elements. The main group includes the elements (except hydrogen, which is sometimes not included) in groups 1 and 2 (s-block), and groups 13 to 18 (p-block).
Group 3 elementGroup 3 is the first group of transition metals in the periodic table. This group is closely related to the rare-earth elements. It contains the four elements scandium (Sc), yttrium (Y), lutetium (Lu), and lawrencium (Lr). The group is also called the scandium group or scandium family after its lightest member. The chemistry of the group 3 elements is typical for early transition metals: they all essentially have only the group oxidation state of +3 as a major one, and like the preceding main-group metals are quite electropositive and have a less rich coordination chemistry.
Cycle graphIn graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with n vertices is called C_n. The number of vertices in C_n equals the number of edges, and every vertex has degree 2; that is, every vertex has exactly two edges incident with it. There are many synonyms for "cycle graph".
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