Question about definition of a graph The Next CEO of Stack OverflowConfusion about the definition of graphsMinnor differences in notation used in definition of graphsgraph vertex chromatic number in a union of 2 sub-graphsDifference between a sub graph and induced sub graph.Multigraph definition confusionDefinition: is a graph allowed to have a “dangling” edge without a vertex at its end(s)?Show that the tree of a connected, nonempty finite graph with $n$ edges has $n+1$ vertices.40 Vertices And A Connected Graph, Minimum Number Of Edges?Fake induction, can't find flaw, every graph with zero edges is connectedExtremal graphs definition
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Question about definition of a graph
The Next CEO of Stack OverflowConfusion about the definition of graphsMinnor differences in notation used in definition of graphsgraph vertex chromatic number in a union of 2 sub-graphsDifference between a sub graph and induced sub graph.Multigraph definition confusionDefinition: is a graph allowed to have a “dangling” edge without a vertex at its end(s)?Show that the tree of a connected, nonempty finite graph with $n$ edges has $n+1$ vertices.40 Vertices And A Connected Graph, Minimum Number Of Edges?Fake induction, can't find flaw, every graph with zero edges is connectedExtremal graphs definition
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By the definition from the book of Kenneth Rosen, we know that a graph consists of a nonempty set of vertices and a set E of edges. Each edges has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints.
From his definition, does it literally mean we actually can form a graph for which the edge has only one vertice on it?
graph-theory
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
$endgroup$
add a comment |
$begingroup$
By the definition from the book of Kenneth Rosen, we know that a graph consists of a nonempty set of vertices and a set E of edges. Each edges has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints.
From his definition, does it literally mean we actually can form a graph for which the edge has only one vertice on it?
graph-theory
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
$endgroup$
3
$begingroup$
I think that would be a loop (an edge going back to connect with the same vertex).
$endgroup$
– Milten
Mar 28 at 9:01
$begingroup$
oh i see. Thanks for the clarification.
$endgroup$
– Ling Min Hao
Mar 28 at 9:05
add a comment |
$begingroup$
By the definition from the book of Kenneth Rosen, we know that a graph consists of a nonempty set of vertices and a set E of edges. Each edges has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints.
From his definition, does it literally mean we actually can form a graph for which the edge has only one vertice on it?
graph-theory
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
$endgroup$
By the definition from the book of Kenneth Rosen, we know that a graph consists of a nonempty set of vertices and a set E of edges. Each edges has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints.
From his definition, does it literally mean we actually can form a graph for which the edge has only one vertice on it?
graph-theory
graph-theory
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
asked Mar 28 at 8:56
Ling Min HaoLing Min Hao
33719
33719
3
$begingroup$
I think that would be a loop (an edge going back to connect with the same vertex).
$endgroup$
– Milten
Mar 28 at 9:01
$begingroup$
oh i see. Thanks for the clarification.
$endgroup$
– Ling Min Hao
Mar 28 at 9:05
add a comment |
3
$begingroup$
I think that would be a loop (an edge going back to connect with the same vertex).
$endgroup$
– Milten
Mar 28 at 9:01
$begingroup$
oh i see. Thanks for the clarification.
$endgroup$
– Ling Min Hao
Mar 28 at 9:05
3
3
$begingroup$
I think that would be a loop (an edge going back to connect with the same vertex).
$endgroup$
– Milten
Mar 28 at 9:01
$begingroup$
I think that would be a loop (an edge going back to connect with the same vertex).
$endgroup$
– Milten
Mar 28 at 9:01
$begingroup$
oh i see. Thanks for the clarification.
$endgroup$
– Ling Min Hao
Mar 28 at 9:05
$begingroup$
oh i see. Thanks for the clarification.
$endgroup$
– Ling Min Hao
Mar 28 at 9:05
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Yes, it does. These so-called loops do indeed have some significant meaning. For example, given a planar graph, the dual graph can contain loops (even if the planar graph was without loops). It is also interesting for the direct product of graphs, see e.g. here.
answered Mar 28 at 12:20
SK19SK19
1,602330
$endgroup$
add a comment |
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1 Answer
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1 Answer
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oldest
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$begingroup$
Yes, it does. These so-called loops do indeed have some significant meaning. For example, given a planar graph, the dual graph can contain loops (even if the planar graph was without loops). It is also interesting for the direct product of graphs, see e.g. here.
answered Mar 28 at 12:20
SK19SK19
1,602330
$endgroup$
add a comment |
$begingroup$
Yes, it does. These so-called loops do indeed have some significant meaning. For example, given a planar graph, the dual graph can contain loops (even if the planar graph was without loops). It is also interesting for the direct product of graphs, see e.g. here.
answered Mar 28 at 12:20
SK19SK19
1,602330
$endgroup$
add a comment |
$begingroup$
Yes, it does. These so-called loops do indeed have some significant meaning. For example, given a planar graph, the dual graph can contain loops (even if the planar graph was without loops). It is also interesting for the direct product of graphs, see e.g. here.
answered Mar 28 at 12:20
SK19SK19
1,602330
$endgroup$
Yes, it does. These so-called loops do indeed have some significant meaning. For example, given a planar graph, the dual graph can contain loops (even if the planar graph was without loops). It is also interesting for the direct product of graphs, see e.g. here.
answered Mar 28 at 12:20
SK19SK19
1,602330
answered Mar 28 at 12:20
SK19SK19
1,602330
answered Mar 28 at 12:20
SK19SK19
1,602330
answered Mar 28 at 12:20
SK19SK19
1,602330
1,602330
add a comment |
add a comment |
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3
$begingroup$
I think that would be a loop (an edge going back to connect with the same vertex).
$endgroup$
– Milten
Mar 28 at 9:01
$begingroup$
oh i see. Thanks for the clarification.
$endgroup$
– Ling Min Hao
Mar 28 at 9:05