4268622
Descrição
Quiz por Will Rickard, atualizado more than 1 year ago
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Criado por Will Rickard
quase 9 anos atrás
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Questão 1
Questão
What is the formal name for the points on a graph?
Responda
-
Vertices
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Edges
Questão 2
Questão
What is the formal name for the lines connecting the points on a graph?
Responda
-
Vertices
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Edges
Questão 3
Questão
V = [blank_start]{a,b,c,d,e}[blank_end]
Responda
-
{a,b,c,d,e}
Questão 4
Questão
E = [blank_start]{{a, b}, {b, c}, {a, c}, {c, d}}[blank_end]
Responda
-
{{a, b}, {b, c}, {a, c}, {c, d}}
Questão 5
Questão
Two graphs are equal if and only if they have the same vertices and the same edges.
Responda
- True
- False
Questão 6
Questão
Two graphs are equal if and only if they have some vertices and the same edges.
Responda
- True
- False
Questão 7
Questão
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.
Responda
-
isomorphic
Questão 8
Questão
The [blank_start]order[blank_end] of a graph G is the number of vertices of G
Responda
-
order
Questão 9
Questão
The order of a graph G is the number of [blank_start]vertices[blank_end] of G
Responda
-
vertices
Questão 10
Questão
The [blank_start]size[blank_end] of G is the number of edges of G
Responda
-
size
Questão 11
Questão
The size of G is the number of [blank_start]edges[blank_end] of G
Responda
-
edges
Questão 12
Questão
We often write [blank_start]uv[blank_end] as shorthand for an edge {u,v}
Responda
-
uv
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{uv}
Questão 13
Questão
We often write uv as shorthand for an edge {[blank_start]u, v[blank_end]}
Responda
-
u,v
Questão 14
Questão
We say that an edge e = uv is [blank_start]incident[blank_end] to the vertices u and v.
Responda
-
incident
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adjacent
Questão 15
Questão
If uv is an edge, we say that the vertices u and v are [blank_start]adjacent[blank_end]
Responda
-
adjacent
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incident
Questão 16
Questão
u is a [blank_start]neighbour[blank_end] of v and that v is a neighbour of u.
Responda
-
neighbour
Questão 17
Questão
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
Responda
-
neighbourhood
Questão 18
Questão
For any vertex v of a graph G, the ............. of v is the set of neighbours of v
Responda
-
neighbourhood N(v)
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neighbourhood N(u)
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compliment N(v)
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neighbourhood G(v)
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neighbourhood d(v)
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neighbourhood N(G)
Questão 19
Questão
We say that v is isolated if it has no [blank_start]neighbours[blank_end].
Responda
-
neighbours
Questão 20
Questão
We say that v is [blank_start]isolated[blank_end] if it has no neighbours.
Responda
-
isolated
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complementary
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distinct
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incident
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adjacent
Questão 21
Questão
The neighbourhood of a is N(a) = [blank_start]{b, c}[blank_end]
Responda
-
{b, c}
Questão 22
Questão
The neighbourhood of d is N (d) = [blank_start]{c}[blank_end]
Responda
-
{c}
Questão 23
Questão
The neighbourhood of e is N(e) = [blank_start]empty[blank_end]
Responda
-
empty
Questão 24
Responda
-
an isolated
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an adjacent
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a
Questão 25
Questão
Vertex e is an [blank_start]isolated[blank_end] vertex
Responda
-
isolated
Questão 26
Questão
The degree of a vertex v in a graph G is d(v) = |N(v)|, that is,
Responda
-
The number of neighbours of v
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The number of edges of v
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The number of vertices of v
-
The number of v
Questão 27
Questão
d(v) =
Responda
-
|N(v)|
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|G(v)|
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0
Questão 28
Questão
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].
Responda
-
2
-
2
-
3
-
1
-
0
Questão 29
Questão
If G is a graph with n vertices, then the degree of each vertex of G is an integer between 0 and n − 1.
Responda
- True
- False
Questão 30
Questão
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].
Responda
-
0
-
n − 1
Questão 31
Questão
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.
Responda
-
degree
Questão 32
Questão
The sum of all vertex degrees is twice the number of edges
Responda
- True
- False
Questão 33
Questão
the sum of all vertex degrees is [blank_start]twice[blank_end] the number of edges
Responda
-
twice
Questão 34
Questão
The sum of all vertex degrees is twice the number of [blank_start]edges[blank_end]
Responda
-
edges
Questão 35
Questão
The sum of all vertex [blank_start]degrees[blank_end] is twice the number of edges
Responda
-
degrees
Questão 36
Questão
In any graph there are an even number of vertices with odd degree.
Responda
- True
- False
Questão 37
Questão
In any graph there are an even number of edges with odd degree.
Responda
- True
- False
Questão 38
Questão
Any graph on at least two vertices has two vertices of the same [blank_start]degree[blank_end].
Responda
-
degree
Questão 39
Questão
The [blank_start]degree sequence[blank_end] of a graph G is the sequence of all degrees of vertices in G
Responda
-
degree sequence
Questão 40
Questão
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.
Responda
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minimum degree
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smallest
Questão 41
Questão
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.
Responda
-
maximum degree
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largest degree
Questão 42
Questão
A graph G is [blank_start]regular[blank_end] if every vertex of G has the same degree
Responda
-
regular
Questão 43
Questão
We say that G is k-regular to mean that every vertex has degree k.
Responda
- True
- False
Questão 44
Questão
We say that G is [blank_start]k[blank_end]-regular to mean that every vertex has degree k.
Responda
-
k
Questão 45
Questão
We say that G is [blank_start]k-regular[blank_end] to mean that every vertex has degree k.
Responda
-
k-regular
Questão 46
Questão
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.
Responda
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subgraph
Questão 47
Questão
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
Responda
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deleting
Questão 48
Questão
H is a [blank_start]spanning[blank_end] subgraph of G if additionally V (H) = V (G), that is, if only edges were deleted.
Responda
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spanning
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"blank"
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copy
Questão 49
Questão
H is a [blank_start]subgraph[blank_end] of a graph G if we can obtain H by deleting vertices and edges of G.
Responda
-
subgraph
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graph
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spanning subgraph
-
copy
Questão 50
Questão
Let G be a graph with δ(G) ≥ 2. Then G contains a cycle.
Responda
- True
- False
Questão 51
Questão
Let G be a graph with δ(G) ≥ 0. Then G contains a cycle.
Responda
- True
- False
Questão 52
Questão
Let G be a graph with N(G) ≥ 2. Then G contains a cycle.
Responda
- True
- False
Questão 53
Questão
Any graph with n vertices and at least n edges contains a cycle
Responda
- True
- False
Questão 54
Questão
Any graph with n vertices and at least n-1 edges contains a cycle
Responda
- True
- False
Questão 55
Questão
Any graph with n+1 vertices and at least n edges contains a cycle
Responda
- True
- False
Questão 56
Questão
The length of W is the number of [blank_start]edges[blank_end] traversed
Responda
-
edges
-
vertices
Questão 57
Questão
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.
Responda
- True
- False
Questão 58
Questão
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.
Responda
- True
- False
Questão 59
Questão
A walk is a path if and only if it has no repeated vertices
Responda
- True
- False
Questão 60
Questão
walk is a path if and only if it has repeated vertices
Responda
- True
- False
Questão 61
Questão
A closed walk is a cycle if and only if the only repeated vertex is the first and last vertex
Responda
- True
- False
Questão 62
Questão
A closed walk is a cycle if and only if there is a repeated vertex at the first and last vertex
Responda
- True
- False
Questão 63
Questão
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.
Responda
-
connected
Questão 64
Questão
A [blank_start]connected component[blank_end] of G is a maximal connected subgraph of G
Responda
-
connected component
-
component
-
subgraph
-
tree
-
cycle
Questão 65
Questão
A tree is a [blank_start]connected[blank_end] [blank_start]acyclic[blank_end] graph.
Responda
-
connected
-
component
-
walk
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path
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unconnected
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join
-
acyclic
-
walks
-
paths
-
cyclic
Questão 66
Questão
A [blank_start]leaf[blank_end] of a tree is a vertex v with d(v) = [blank_start]1[blank_end].
Responda
-
leaf
-
edge
-
vertex
-
1
-
2
-
0
-
5
Questão 67
Questão
Any tree on n ≥ 2 vertices has a leaf.
Responda
- True
- False
Questão 68
Questão
Any tree on n ≥ 0 vertices has a leaf.
Responda
- True
- False
Questão 69
Questão
Any connected graph contains a spanning tree
Responda
- True
- False
Questão 70
Questão
Any connected graph on n vertices with precisely n − 1 edges is a tree
Responda
- True
- False
Questão 71
Questão
Any connected graph on n vertices with precisely n edges is a tree
Responda
- True
- False
Questão 72
Questão
Any acyclic graph on n vertices with precisely n − 1 edges is a tree.
Responda
- True
- False
Questão 73
Questão
Any acyclic graph on n vertices with precisely n edges is a tree.
Responda
- True
- False
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