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