Question 1
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What is the formal name for the points on a graph?
Question 2
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What is the formal name for the lines connecting the points on a graph?
Question 3
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V = [blank_start]{a,b,c,d,e}[blank_end]
Question 4
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E = [blank_start]{{a, b}, {b, c}, {a, c}, {c, d}}[blank_end]
Answer

{{a, b}, {b, c}, {a, c}, {c, d}}
Question 5
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Two graphs are equal if and only if they have the same vertices and the same edges.
Question 6
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Two graphs are equal if and only if they have some vertices and the same edges.
Question 7
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We say that two graphs G and H are [blank_start]isomorphic[blank_end] if we can relabel the vertices of G to obtain H.
Question 8
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The [blank_start]order[blank_end] of a graph G is the number of vertices of G
Question 9
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The order of a graph G is the number of [blank_start]vertices[blank_end] of G
Question 10
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The [blank_start]size[blank_end] of G is the number of edges of G
Question 11
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The size of G is the number of [blank_start]edges[blank_end] of G
Question 12
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We often write [blank_start]uv[blank_end] as shorthand for an edge {u,v}
Question 13
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We often write uv as shorthand for an edge {[blank_start]u, v[blank_end]}
Question 14
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We say that an edge e = uv is [blank_start]incident[blank_end] to the vertices u and v.
Question 15
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If uv is an edge, we say that the vertices u and v are [blank_start]adjacent[blank_end]
Question 16
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u is a [blank_start]neighbour[blank_end] of v and that v is a neighbour of u.
Question 17
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For any vertex v of a graph G, the [blank_start]neighbourhood[blank_end] N(v) of v is the set of neighbours of v
Question 18
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For any vertex v of a graph G, the ............. of v is the set of neighbours of v
Answer

neighbourhood N(v)

neighbourhood N(u)

compliment N(v)

neighbourhood G(v)

neighbourhood d(v)

neighbourhood N(G)
Question 19
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We say that v is isolated if it has no [blank_start]neighbours[blank_end].
Question 20
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We say that v is [blank_start]isolated[blank_end] if it has no neighbours.
Answer

isolated

complementary

distinct

incident

adjacent
Question 21
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The neighbourhood of a is N(a) = [blank_start]{b, c}[blank_end]
Question 22
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The neighbourhood of d is N (d) = [blank_start]{c}[blank_end]
Question 23
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The neighbourhood of e is N(e) = [blank_start]empty[blank_end]
Question 24
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Vertex e is ........ vertex
Answer

an isolated

an adjacent

a
Question 25
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Vertex e is an [blank_start]isolated[blank_end] vertex
Question 26
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The degree of a vertex v in a graph G is d(v) = N(v), that is,
Question 27
Question 28
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The vertex degrees are
d(a) = [blank_start]2[blank_end],
d(b) = [blank_start]2[blank_end],
d(c) = [blank_start]3[blank_end],
d(d) = [blank_start]1[blank_end]
d(e) = [blank_start]0[blank_end].
Question 29
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If G is a graph with n vertices, then the degree of each vertex of G is an integer between 0 and n − 1.
Question 30
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If G is a graph with n vertices, then the degree of each vertex of G is an integer between [blank_start]0[blank_end] and [blank_start]n − 1[blank_end].
Question 31
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If G is a graph with n vertices, then the [blank_start]degree[blank_end] of each vertex of G is an integer between 0 and n − 1.
Question 32
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The sum of all vertex degrees is twice the number of edges
Question 33
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the sum of all vertex degrees is [blank_start]twice[blank_end] the number of edges
Question 34
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The sum of all vertex degrees is twice the number of [blank_start]edges[blank_end]
Question 35
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The sum of all vertex [blank_start]degrees[blank_end] is twice the number of edges
Question 36
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In any graph there are an even number of vertices with odd degree.
Question 37
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In any graph there are an even number of edges with odd degree.
Question 38
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Any graph on at least two vertices has two vertices of the same [blank_start]degree[blank_end].
Question 39
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The [blank_start]degree sequence[blank_end] of a graph G is the sequence of all degrees of vertices in G
Question 40
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The [blank_start]minimum degree[blank_end] of a graph G, denoted δ(G), is the [blank_start]smallest[blank_end] degree of a vertex of G.
Question 41
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The [blank_start]maximum degree[blank_end] of a graph G, denoted ∆(G), is the [blank_start]largest degree[blank_end] of a vertex of G.
Answer

maximum degree

largest degree
Question 42
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A graph G is [blank_start]regular[blank_end] if every vertex of G has the same degree
Question 43
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We say that G is kregular to mean that every vertex has degree k.
Question 44
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We say that G is [blank_start]k[blank_end]regular to mean that every vertex has degree k.
Question 45
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We say that G is [blank_start]kregular[blank_end] to mean that every vertex has degree k.
Question 46
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A graph H is a [blank_start]subgraph[blank_end] of a graph G if we can obtain H by deleting vertices and edges of G.
Question 47
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A graph H is a subgraph of a graph G if we can obtain H by [blank_start]deleting[blank_end] vertices and edges of G
Question 48
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H is a [blank_start]spanning[blank_end] subgraph of G if additionally V (H) = V (G), that is, if only edges were deleted.
Question 49
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H is a [blank_start]subgraph[blank_end] of a graph G if we can obtain H by deleting vertices and edges of G.
Answer

subgraph

graph

spanning subgraph

copy
Question 50
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Let G be a graph with δ(G) ≥ 2. Then G contains a cycle.
Question 51
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Let G be a graph with δ(G) ≥ 0. Then G contains a cycle.
Question 52
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Let G be a graph with N(G) ≥ 2. Then G contains a cycle.
Question 53
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Any graph with n vertices and at least n edges contains a cycle
Question 54
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Any graph with n vertices and at least n1 edges contains a cycle
Question 55
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Any graph with n+1 vertices and at least n edges contains a cycle
Question 56
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The length of W is the number of [blank_start]edges[blank_end] traversed
Question 57
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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.
Question 58
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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.
Question 59
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A walk is a path if and only if it has no repeated vertices
Question 60
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walk is a path if and only if it has repeated vertices
Question 61
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A closed walk is a cycle if and only if the only repeated vertex is the first and last vertex
Question 62
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A closed walk is a cycle if and only if there is a repeated vertex at the first and last vertex
Question 63
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A graph G is [blank_start]connected[blank_end] if for any two vertices u and v of G there is a walk in G from u to v.
Question 64
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A [blank_start]connected component[blank_end] of G is a maximal connected subgraph of G
Answer

connected component

component

subgraph

tree

cycle
Question 65
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A tree is a [blank_start]connected[blank_end] [blank_start]acyclic[blank_end] graph.
Answer

connected

component

walk

path

unconnected

join

acyclic

walks

paths

cyclic
Question 66
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A [blank_start]leaf[blank_end] of a tree is a vertex v with d(v) = [blank_start]1[blank_end].
Question 67
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Any tree on n ≥ 2 vertices has a leaf.
Question 68
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Any tree on n ≥ 0 vertices has a leaf.
Question 69
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Any connected graph contains a spanning tree
Question 70
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Any connected graph on n vertices with precisely n − 1 edges is a tree
Question 71
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Any connected graph on n vertices with precisely n edges is a tree
Question 72
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Any acyclic graph on n vertices with precisely n − 1 edges is a tree.
Question 73
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Any acyclic graph on n vertices with precisely n edges is a tree.