D1 graphs

Question 1

Edge

Answer 1

Has a vertex at each end. An edge with the same vertex at each end is called a loop.

Question 2

Degree

Answer 2

(Or order) of a vertex is the number of edges incident on it.

Question 3

Simple graph

Answer 3

No loops, and in which there is no more than one edge connecting any pair of vertices.

Question 4

Walk

Answer 4

A sequence of edges in which the end of one edge (except the last) is the beginning of the next.

Question 5

Trail

Answer 5

Is a walk in which no edge is repeated.

Question 6

Path

Answer 6

Is a trail in which no vertex is repeated.

Question 7

Cycle

Answer 7

A closed path

Question 8

Hamiltonian cycle

Answer 8

A cycle which visits every vertex.

Question 9

Tree

Answer 9

Simple connected graph with no cycles.

Question 10

Digraph

Answer 10

Graph in which at least one edge has a direction associated with it.

Question 11

Complete graph

Answer 11

Simple graph which every pair of vertices is connected with an edge.

Question 12

Incidence matrix

Answer 12

Represents a graph with a matrix.

Question 13

Isomorphic

Answer 13

Same graph in a different structure.

Question 14

Planar graph

Answer 14

Drawn with no edges crossing

Question 15

Bipartite graph

Answer 15

Vertices fall into two sets and in which each edge has a vertex from one set at one end and from the other set at its other end.

Question 16

Graph

Answer 16

A set of vertices (or nodes), one for each member of X, together with a set of edges (or arcs).