What is the formal name for the points on a graph?

Vertices

Edges

What is the formal name for the lines connecting the points on a graph?

V =

E =

Two graphs are equal if and only if they have the same vertices and the same edges.

Two graphs are equal if and only if they have some vertices and the same edges.

We say that two graphs G and H are if we can relabel the vertices of G to obtain H.

The of a graph G is the number of vertices of G

The order of a graph G is the number of of G

The of G is the number of edges of G

The size of G is the number of of G

We often write as shorthand for an edge {u,v}

We often write uv as shorthand for an edge {}

We say that an edge e = uv is incident adjacent( incident, adjacent ) to the vertices u and v.

If uv is an edge, we say that the vertices u and v are adjacent incident( adjacent, incident )

u is a of v and that v is a neighbour of u.

For any vertex v of a graph G, the N(v) of v is the set of neighbours of v

For any vertex v of a graph G, the ............. of v is the set of neighbours of v

neighbourhood N(v)

neighbourhood N(u)

compliment N(v)

neighbourhood G(v)

neighbourhood d(v)

neighbourhood N(G)

We say that v is isolated if it has no .

We say that v is isolated complementary distinct incident adjacent( isolated, complementary, distinct, incident, adjacent ) if it has no neighbours.

The neighbourhood of a is N(a) =

The neighbourhood of d is N (d) =

The neighbourhood of e is N(e) =

Vertex e is ........ vertex

an isolated

an adjacent

a

Vertex e is an vertex

The degree of a vertex v in a graph G is d(v) = |N(v)|, that is,

The number of neighbours of v

The number of edges of v

The number of vertices of v

The number of v

d(v) =

|N(v)|

|G(v)|

0

The vertex degrees are d(a) = , d(b) = , d(c) = , d(d) = d(e) = .

If G is a graph with n vertices, then the degree of each vertex of G is an integer between 0 and n − 1.

If G is a graph with n vertices, then the degree of each vertex of G is an integer between and .

If G is a graph with n vertices, then the of each vertex of G is an integer between 0 and n − 1.

The sum of all vertex degrees is twice the number of edges

the sum of all vertex degrees is the number of edges

The sum of all vertex degrees is twice the number of

The sum of all vertex is twice the number of edges

In any graph there are an even number of vertices with odd degree.

In any graph there are an even number of edges with odd degree.

Any graph on at least two vertices has two vertices of the same .

The of a graph G is the sequence of all degrees of vertices in G

The of a graph G, denoted δ(G), is the degree of a vertex of G.

The of a graph G, denoted ∆(G), is the of a vertex of G.

A graph G is if every vertex of G has the same degree

We say that G is k-regular to mean that every vertex has degree k.

We say that G is -regular to mean that every vertex has degree k.

We say that G is to mean that every vertex has degree k.

A graph H is a of a graph G if we can obtain H by deleting vertices and edges of G.

A graph H is a subgraph of a graph G if we can obtain H by vertices and edges of G

H is a spanning "blank" copy( spanning, "blank", copy ) subgraph of G if additionally V (H) = V (G), that is, if only edges were deleted.

H is a subgraph graph spanning subgraph copy( subgraph, graph, spanning subgraph, copy ) of a graph G if we can obtain H by deleting vertices and edges of G.

Let G be a graph with δ(G) ≥ 2. Then G contains a cycle.

Let G be a graph with δ(G) ≥ 0. Then G contains a cycle.

Let G be a graph with N(G) ≥ 2. Then G contains a cycle.

Any graph with n vertices and at least n edges contains a cycle

Any graph with n vertices and at least n-1 edges contains a cycle

Any graph with n+1 vertices and at least n edges contains a cycle

The length of W is the number of edges vertices( edges, vertices ) traversed

A walk is closed if the first and last vertices of the walk are the same, that is, if you finish at the same vertex at which you started.

A walk is open if the first and last vertices of the walk are the same, that is, if you finish at the same vertex at which you started.

A walk is a path if and only if it has no repeated vertices

walk is a path if and only if it has repeated vertices

A closed walk is a cycle if and only if the only repeated vertex is the first and last vertex

A closed walk is a cycle if and only if there is a repeated vertex at the first and last vertex

A graph G is if for any two vertices u and v of G there is a walk in G from u to v.

A of G is a maximal connected subgraph of G

A tree is a graph.

A of a tree is a vertex v with d(v) = .

Any tree on n ≥ 2 vertices has a leaf.

Any tree on n ≥ 0 vertices has a leaf.

Any connected graph contains a spanning tree

Any connected graph on n vertices with precisely n − 1 edges is a tree

Any connected graph on n vertices with precisely n edges is a tree

Any acyclic graph on n vertices with precisely n − 1 edges is a tree.

Any acyclic graph on n vertices with precisely n edges is a tree.