**Some graph vocabulary: join, adjacent, incident, complete, size, order**

When two vertices of a graph are connected by an edge, these vertices are said to be *adjacent*, and the edge is said to *join* them.

When two edges meet at the same vertex, those two edges are said to be *adjacent*.

A vertex and an edge that touch one another are said to be *incident* to one another. Each is said to be *on* the other.

The term *size* refers to the number of edges in a graph. The number of vertices in the graph is called its *order*.

Each of these graphs is of order 6 and size 8. By a common notational convention, these graphs are referred to as (6,8) graphs.

A *complete graph* is a graph in which all vertices are adjacent to one another.

K(4) |
K(5) |
K(6) |
K(7) |

A *trivial* graph is a graph with a single vertex. All other graphs are *nontrivial*.

This is a (5,7) graph. It has order 5 and size 7. The two green edges are adjacent. The two red vertices are adjacent; they are joined by the blue edge. The blue edge is incident on the red vertices. The degree of the yellow vertex is 4. This is not a complete graph because not all the vertices are adjacent.

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