Complete graph in the context of Directed graph

In graph theory, the hypercube graph ${\displaystyle Q_{n}}$ is the edge graph of the ${\displaystyle n}$-dimensional hypercube, that is, it is the graph formed from the vertices and edges of the hypercube. For instance, the cube graph ${\displaystyle Q_{3}}$ is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube.${\displaystyle Q_{n}}$ has ${\displaystyle 2^{n}}$ vertices, ${\displaystyle 2^{n-1}n}$ edges, and is a regular graph with ${\displaystyle n}$ edges touching each vertex.

The hypercube graph ${\displaystyle Q_{n}}$ may also be constructed by creating a vertex for each subset of an ${\displaystyle n}$-element set, with two vertices adjacent when their subsets differ in a single element, or by creating a vertex for each ${\displaystyle n}$-digit binary number, with two vertices adjacent when their binary representations differ in a single digit. It is the ${\displaystyle n}$-fold Cartesian product of the two-vertex complete graph, and may be decomposed into two copies of ${\displaystyle Q_{n-1}}$ connected to each other by a perfect matching.

In graph theory, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph.It is analogous to the disjoint union of sets and is constructed by making the vertex set of the result be the disjoint union of the vertex sets of the given graphs and by making the edge set of the result be the disjoint union of the edge sets of the given graphs. Any disjoint union of two or more nonempty graphs is necessarily disconnected.

In 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.

Cycle graph ${\displaystyle C_{1}}$ is an isolated loop. Cycle graph ${\displaystyle C_{3}}$ is the same as complete graph ${\displaystyle K_{3}}$.

In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. The degree of a vertex ${\displaystyle v}$ is denoted ${\displaystyle \deg(v)}$ or ${\displaystyle \deg v}$. The maximum degree of a graph ${\displaystyle G}$ is denoted by ${\displaystyle \Delta (G)}$, and is the maximum of ${\displaystyle G}$'s vertices' degrees. The minimum degree of a graph is denoted by ${\displaystyle \delta (G)}$, and is the minimum of ${\displaystyle G}$'s vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0.

In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph. A complete graph (denoted ${\displaystyle K_{n}}$, where ${\displaystyle n}$ is the number of vertices in the graph) is a special kind of regular graph where all vertices have the maximum possible degree, ${\displaystyle n-1}$.