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Clarification on definition of a term in graph theory.
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I was going through some literature regarding Generalized Petersen graphs $P(n,k)$. Some authors considered $k < n$ and others took $k<fracn2$. I am quite confused and don't have any idea which definition to pick for my work?
Kindly help me in this regard. Thanks a lot for your kind help.
combinatorics discrete-mathematics graph-theory terminology definition
asked Jul 18 at 4:23
monalisa
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up vote
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I was going through some literature regarding Generalized Petersen graphs $P(n,k)$. Some authors considered $k < n$ and others took $k<fracn2$. I am quite confused and don't have any idea which definition to pick for my work?
Kindly help me in this regard. Thanks a lot for your kind help.
combinatorics discrete-mathematics graph-theory terminology definition
asked Jul 18 at 4:23
monalisa
1,34111835
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I was going through some literature regarding Generalized Petersen graphs $P(n,k)$. Some authors considered $k < n$ and others took $k<fracn2$. I am quite confused and don't have any idea which definition to pick for my work?
Kindly help me in this regard. Thanks a lot for your kind help.
combinatorics discrete-mathematics graph-theory terminology definition
asked Jul 18 at 4:23
monalisa
1,34111835
I was going through some literature regarding Generalized Petersen graphs $P(n,k)$. Some authors considered $k < n$ and others took $k<fracn2$. I am quite confused and don't have any idea which definition to pick for my work?
Kindly help me in this regard. Thanks a lot for your kind help.
combinatorics discrete-mathematics graph-theory terminology definition
asked Jul 18 at 4:23
monalisa
1,34111835
asked Jul 18 at 4:23
monalisa
1,34111835
asked Jul 18 at 4:23
monalisa
1,34111835
asked Jul 18 at 4:23
monalisa
1,34111835
1,34111835
add a comment |Â
add a comment |Â
1 Answer
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It doesn't matter. If we allow $k > n/2$, we don't gain any generality, since $P(n,k)$ is the same graph as $P(n,n-k)$.
I guess that for even $n$, $P(n,n/2)$ is a graph only allowed by one of the definitions, but it's not a particularly interesting graph. Whether or not you want to allow it in the work you're doing presumably depends on what you're trying to do.
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
It doesn't matter. If we allow $k > n/2$, we don't gain any generality, since $P(n,k)$ is the same graph as $P(n,n-k)$.
I guess that for even $n$, $P(n,n/2)$ is a graph only allowed by one of the definitions, but it's not a particularly interesting graph. Whether or not you want to allow it in the work you're doing presumably depends on what you're trying to do.
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
add a comment |Â
up vote
3
down vote
It doesn't matter. If we allow $k > n/2$, we don't gain any generality, since $P(n,k)$ is the same graph as $P(n,n-k)$.
I guess that for even $n$, $P(n,n/2)$ is a graph only allowed by one of the definitions, but it's not a particularly interesting graph. Whether or not you want to allow it in the work you're doing presumably depends on what you're trying to do.
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
add a comment |Â
up vote
3
down vote
up vote
3
down vote
It doesn't matter. If we allow $k > n/2$, we don't gain any generality, since $P(n,k)$ is the same graph as $P(n,n-k)$.
I guess that for even $n$, $P(n,n/2)$ is a graph only allowed by one of the definitions, but it's not a particularly interesting graph. Whether or not you want to allow it in the work you're doing presumably depends on what you're trying to do.
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
It doesn't matter. If we allow $k > n/2$, we don't gain any generality, since $P(n,k)$ is the same graph as $P(n,n-k)$.
I guess that for even $n$, $P(n,n/2)$ is a graph only allowed by one of the definitions, but it's not a particularly interesting graph. Whether or not you want to allow it in the work you're doing presumably depends on what you're trying to do.
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
answered Jul 18 at 4:34
Misha Lavrov
35.6k44690
35.6k44690
add a comment |Â
add a comment |Â
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