How to properly sort the definitions of null, trivial and empty graph?
0
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I have just started learning about graphs by Saha Ray's book and I am confused by having these definitions that seem to be somewhat related:
Null graph (on page $5$): If $E = varnothing$ in a graph $G = (V, E)$, then such a graph without any edges is called a null graph.
Empty graph (page $7$): An empty (or trivial) graph is a graph with no edges.
Trivial graph (page $14$): A graph $G=(V,E)$ is trivial, if it has only one vertex. Otherwise $G$ is nontrivial.
Now, could I sort my knowledge in this way?
- Null-graph = Empty graph: has no edges (no matter how many vertices)
- Trivial graph: is a Null-graph (=empty graph) with only a single vertex,
As long as I could understand, speaking about a graph without any vertices won't make sense, as there is nothing to speak about in that case!
Edit: On the $12$th page I can read:
- If $G_1$ and $G_2$ are vertex disjoint, then $G_1 cap G_2$ is empty.
So I must update my fact-sorting this way:
Null graph: $|V| geq 1$, $|E| = 0$.
Trivial graph: $|V| = 1$.
Empty graph: $|V| = 0$.
graph-theory
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
asked Apr 10 '18 at 17:15
higraphshigraphs
11
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add a comment |
0
$begingroup$
I have just started learning about graphs by Saha Ray's book and I am confused by having these definitions that seem to be somewhat related:
Null graph (on page $5$): If $E = varnothing$ in a graph $G = (V, E)$, then such a graph without any edges is called a null graph.
Empty graph (page $7$): An empty (or trivial) graph is a graph with no edges.
Trivial graph (page $14$): A graph $G=(V,E)$ is trivial, if it has only one vertex. Otherwise $G$ is nontrivial.
Now, could I sort my knowledge in this way?
- Null-graph = Empty graph: has no edges (no matter how many vertices)
- Trivial graph: is a Null-graph (=empty graph) with only a single vertex,
As long as I could understand, speaking about a graph without any vertices won't make sense, as there is nothing to speak about in that case!
Edit: On the $12$th page I can read:
- If $G_1$ and $G_2$ are vertex disjoint, then $G_1 cap G_2$ is empty.
So I must update my fact-sorting this way:
Null graph: $|V| geq 1$, $|E| = 0$.
Trivial graph: $|V| = 1$.
Empty graph: $|V| = 0$.
graph-theory
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
asked Apr 10 '18 at 17:15
higraphshigraphs
11
$endgroup$
$begingroup$
I believe that such distinctions in terminology are properly at the author's discretion. It is good that you pick up on the slight inconsistency in meaning for "trivial graph". The author seems to have abused their discretion a bit in this case, but I don't think there is a "higher authority" we can appeal to.
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– hardmath
Apr 10 '18 at 17:21
$begingroup$
Thank you very much!
$endgroup$
– higraphs
Apr 10 '18 at 19:43
add a comment |
0
0
0
$begingroup$
I have just started learning about graphs by Saha Ray's book and I am confused by having these definitions that seem to be somewhat related:
Null graph (on page $5$): If $E = varnothing$ in a graph $G = (V, E)$, then such a graph without any edges is called a null graph.
Empty graph (page $7$): An empty (or trivial) graph is a graph with no edges.
Trivial graph (page $14$): A graph $G=(V,E)$ is trivial, if it has only one vertex. Otherwise $G$ is nontrivial.
Now, could I sort my knowledge in this way?
- Null-graph = Empty graph: has no edges (no matter how many vertices)
- Trivial graph: is a Null-graph (=empty graph) with only a single vertex,
As long as I could understand, speaking about a graph without any vertices won't make sense, as there is nothing to speak about in that case!
Edit: On the $12$th page I can read:
- If $G_1$ and $G_2$ are vertex disjoint, then $G_1 cap G_2$ is empty.
So I must update my fact-sorting this way:
Null graph: $|V| geq 1$, $|E| = 0$.
Trivial graph: $|V| = 1$.
Empty graph: $|V| = 0$.
graph-theory
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
asked Apr 10 '18 at 17:15
higraphshigraphs
11
$endgroup$
I have just started learning about graphs by Saha Ray's book and I am confused by having these definitions that seem to be somewhat related:
Null graph (on page $5$): If $E = varnothing$ in a graph $G = (V, E)$, then such a graph without any edges is called a null graph.
Empty graph (page $7$): An empty (or trivial) graph is a graph with no edges.
Trivial graph (page $14$): A graph $G=(V,E)$ is trivial, if it has only one vertex. Otherwise $G$ is nontrivial.
Now, could I sort my knowledge in this way?
- Null-graph = Empty graph: has no edges (no matter how many vertices)
- Trivial graph: is a Null-graph (=empty graph) with only a single vertex,
As long as I could understand, speaking about a graph without any vertices won't make sense, as there is nothing to speak about in that case!
Edit: On the $12$th page I can read:
- If $G_1$ and $G_2$ are vertex disjoint, then $G_1 cap G_2$ is empty.
So I must update my fact-sorting this way:
Null graph: $|V| geq 1$, $|E| = 0$.
Trivial graph: $|V| = 1$.
Empty graph: $|V| = 0$.
graph-theory
graph-theory
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
asked Apr 10 '18 at 17:15
higraphshigraphs
11
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
asked Apr 10 '18 at 17:15
higraphshigraphs
11
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
edited Dec 5 '18 at 1:55
Rócherz
2,7762721
2,7762721
asked Apr 10 '18 at 17:15
higraphshigraphs
11
asked Apr 10 '18 at 17:15
higraphshigraphs
11
asked Apr 10 '18 at 17:15
higraphshigraphs
11
11
$begingroup$
I believe that such distinctions in terminology are properly at the author's discretion. It is good that you pick up on the slight inconsistency in meaning for "trivial graph". The author seems to have abused their discretion a bit in this case, but I don't think there is a "higher authority" we can appeal to.
$endgroup$
– hardmath
Apr 10 '18 at 17:21
$begingroup$
Thank you very much!
$endgroup$
– higraphs
Apr 10 '18 at 19:43
add a comment |
$begingroup$
I believe that such distinctions in terminology are properly at the author's discretion. It is good that you pick up on the slight inconsistency in meaning for "trivial graph". The author seems to have abused their discretion a bit in this case, but I don't think there is a "higher authority" we can appeal to.
$endgroup$
– hardmath
Apr 10 '18 at 17:21
$begingroup$
Thank you very much!
$endgroup$
– higraphs
Apr 10 '18 at 19:43
$begingroup$
I believe that such distinctions in terminology are properly at the author's discretion. It is good that you pick up on the slight inconsistency in meaning for "trivial graph". The author seems to have abused their discretion a bit in this case, but I don't think there is a "higher authority" we can appeal to.
$endgroup$
– hardmath
Apr 10 '18 at 17:21
$begingroup$
I believe that such distinctions in terminology are properly at the author's discretion. It is good that you pick up on the slight inconsistency in meaning for "trivial graph". The author seems to have abused their discretion a bit in this case, but I don't think there is a "higher authority" we can appeal to.
$endgroup$
– hardmath
Apr 10 '18 at 17:21
$begingroup$
Thank you very much!
$endgroup$
– higraphs
Apr 10 '18 at 19:43
$begingroup$
Thank you very much!
$endgroup$
– higraphs
Apr 10 '18 at 19:43
add a comment |
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I believe that such distinctions in terminology are properly at the author's discretion. It is good that you pick up on the slight inconsistency in meaning for "trivial graph". The author seems to have abused their discretion a bit in this case, but I don't think there is a "higher authority" we can appeal to.
$endgroup$
– hardmath
Apr 10 '18 at 17:21
$begingroup$
Thank you very much!
$endgroup$
– higraphs
Apr 10 '18 at 19:43