What are Distance Regular Graphs
Clash Royale CLAN TAG#URR8PPP
up vote
4
down vote
favorite
I have been trying to understand distance regular graphs and how to compute the intersection array.
Distance Regular Graphs, this is the resource I have used. I could not figure what is br in δ(v,u)=r.br
Secondly cr in cr is the number of vertices that are adjacent to u and a distance of r − 1 from v
Lastly the two clauses for intersection array in the given link.
​
P.S : I need its concept to understand a paper, would appreciate the help
combinatorics graph-theory
asked Aug 29 at 7:37
sachal
254
add a comment |Â
up vote
4
down vote
favorite
I have been trying to understand distance regular graphs and how to compute the intersection array.
Distance Regular Graphs, this is the resource I have used. I could not figure what is br in δ(v,u)=r.br
Secondly cr in cr is the number of vertices that are adjacent to u and a distance of r − 1 from v
Lastly the two clauses for intersection array in the given link.
​
P.S : I need its concept to understand a paper, would appreciate the help
combinatorics graph-theory
asked Aug 29 at 7:37
sachal
254
The author is violating an important tenet of mathematical writing: Never start a sentence with a symbol. In the last paragraph of page 3, one sentence reads "Distance regular graphs have an intersection array [...] where for any two vertices $v$ and $u$ that are $r$ distance apart, $delta(v,u) = r$." (This seems to be the author's way of defining $delta$, although the phrasing could be better.) The immediately-following $b_r$ is the start of the next sentence, it is not being multiplied by the $r$. Does that help?
– Blue
Aug 29 at 8:19
1
Yes thanks! a silly misunderstanding anyway.
– sachal
Aug 29 at 8:59
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
I have been trying to understand distance regular graphs and how to compute the intersection array.
Distance Regular Graphs, this is the resource I have used. I could not figure what is br in δ(v,u)=r.br
Secondly cr in cr is the number of vertices that are adjacent to u and a distance of r − 1 from v
Lastly the two clauses for intersection array in the given link.
​
P.S : I need its concept to understand a paper, would appreciate the help
combinatorics graph-theory
asked Aug 29 at 7:37
sachal
254
I have been trying to understand distance regular graphs and how to compute the intersection array.
Distance Regular Graphs, this is the resource I have used. I could not figure what is br in δ(v,u)=r.br
Secondly cr in cr is the number of vertices that are adjacent to u and a distance of r − 1 from v
Lastly the two clauses for intersection array in the given link.
​
P.S : I need its concept to understand a paper, would appreciate the help
combinatorics graph-theory
asked Aug 29 at 7:37
sachal
254
asked Aug 29 at 7:37
sachal
254
asked Aug 29 at 7:37
sachal
254
asked Aug 29 at 7:37
sachal
254
254
The author is violating an important tenet of mathematical writing: Never start a sentence with a symbol. In the last paragraph of page 3, one sentence reads "Distance regular graphs have an intersection array [...] where for any two vertices $v$ and $u$ that are $r$ distance apart, $delta(v,u) = r$." (This seems to be the author's way of defining $delta$, although the phrasing could be better.) The immediately-following $b_r$ is the start of the next sentence, it is not being multiplied by the $r$. Does that help?
– Blue
Aug 29 at 8:19
1
Yes thanks! a silly misunderstanding anyway.
– sachal
Aug 29 at 8:59
add a comment |Â
The author is violating an important tenet of mathematical writing: Never start a sentence with a symbol. In the last paragraph of page 3, one sentence reads "Distance regular graphs have an intersection array [...] where for any two vertices $v$ and $u$ that are $r$ distance apart, $delta(v,u) = r$." (This seems to be the author's way of defining $delta$, although the phrasing could be better.) The immediately-following $b_r$ is the start of the next sentence, it is not being multiplied by the $r$. Does that help?
– Blue
Aug 29 at 8:19
1
Yes thanks! a silly misunderstanding anyway.
– sachal
Aug 29 at 8:59
The author is violating an important tenet of mathematical writing: Never start a sentence with a symbol. In the last paragraph of page 3, one sentence reads "Distance regular graphs have an intersection array [...] where for any two vertices $v$ and $u$ that are $r$ distance apart, $delta(v,u) = r$." (This seems to be the author's way of defining $delta$, although the phrasing could be better.) The immediately-following $b_r$ is the start of the next sentence, it is not being multiplied by the $r$. Does that help?
– Blue
Aug 29 at 8:19
The author is violating an important tenet of mathematical writing: Never start a sentence with a symbol. In the last paragraph of page 3, one sentence reads "Distance regular graphs have an intersection array [...] where for any two vertices $v$ and $u$ that are $r$ distance apart, $delta(v,u) = r$." (This seems to be the author's way of defining $delta$, although the phrasing could be better.) The immediately-following $b_r$ is the start of the next sentence, it is not being multiplied by the $r$. Does that help?
– Blue
Aug 29 at 8:19
1
1
Yes thanks! a silly misunderstanding anyway.
– sachal
Aug 29 at 8:59
Yes thanks! a silly misunderstanding anyway.
– sachal
Aug 29 at 8:59
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
Quoting the paper, with some hopefully helpful comments in red.
Distance regular graphs have an intersection array $b_0,b_1,ldots,b_d−1;c_1,c_2, ldots,c_d$ where for any two vertices $v$ and $u$ that are $r$ distance apart, $δ(v,u) = r$.$colorredleftarrow texta period.$ $b_r$ is the number of vertices that are adjacent to $u$ and at a distance $r + 1$ to $v$.$colorredleftarrow textanother period.$ $c_r$ is the number of vertices that are adjacent to $u$ and a distance of $r − 1$ from $v$.
The definition should be clear now.
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Quoting the paper, with some hopefully helpful comments in red.
Distance regular graphs have an intersection array $b_0,b_1,ldots,b_d−1;c_1,c_2, ldots,c_d$ where for any two vertices $v$ and $u$ that are $r$ distance apart, $δ(v,u) = r$.$colorredleftarrow texta period.$ $b_r$ is the number of vertices that are adjacent to $u$ and at a distance $r + 1$ to $v$.$colorredleftarrow textanother period.$ $c_r$ is the number of vertices that are adjacent to $u$ and a distance of $r − 1$ from $v$.
The definition should be clear now.
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
add a comment |Â
up vote
2
down vote
accepted
Quoting the paper, with some hopefully helpful comments in red.
Distance regular graphs have an intersection array $b_0,b_1,ldots,b_d−1;c_1,c_2, ldots,c_d$ where for any two vertices $v$ and $u$ that are $r$ distance apart, $δ(v,u) = r$.$colorredleftarrow texta period.$ $b_r$ is the number of vertices that are adjacent to $u$ and at a distance $r + 1$ to $v$.$colorredleftarrow textanother period.$ $c_r$ is the number of vertices that are adjacent to $u$ and a distance of $r − 1$ from $v$.
The definition should be clear now.
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Quoting the paper, with some hopefully helpful comments in red.
Distance regular graphs have an intersection array $b_0,b_1,ldots,b_d−1;c_1,c_2, ldots,c_d$ where for any two vertices $v$ and $u$ that are $r$ distance apart, $δ(v,u) = r$.$colorredleftarrow texta period.$ $b_r$ is the number of vertices that are adjacent to $u$ and at a distance $r + 1$ to $v$.$colorredleftarrow textanother period.$ $c_r$ is the number of vertices that are adjacent to $u$ and a distance of $r − 1$ from $v$.
The definition should be clear now.
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
Quoting the paper, with some hopefully helpful comments in red.
Distance regular graphs have an intersection array $b_0,b_1,ldots,b_d−1;c_1,c_2, ldots,c_d$ where for any two vertices $v$ and $u$ that are $r$ distance apart, $δ(v,u) = r$.$colorredleftarrow texta period.$ $b_r$ is the number of vertices that are adjacent to $u$ and at a distance $r + 1$ to $v$.$colorredleftarrow textanother period.$ $c_r$ is the number of vertices that are adjacent to $u$ and a distance of $r − 1$ from $v$.
The definition should be clear now.
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
answered Aug 29 at 8:20
J.-E. Pin
17.4k21753
17.4k21753
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
add a comment |Â
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
yes i got it now but what the entries of intersection array represent? Are those the number of vertices adjacent to you I am assuming $$b_0 , b_1,...,b_d-1 = b_r$$
– sachal
Aug 29 at 9:05
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
$d$ is the dimension of the graph. Thus the entries of the "intersection array" are the successive values of the $b_r$'s ($0 leqslant r leqslant d-1$) followed by the successive values of the $c_r$'s ($1 leqslant r leqslant d$).
– J.-E. Pin
Aug 29 at 9:09
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2898057%2fwhat-are-distance-regular-graphs%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
The author is violating an important tenet of mathematical writing: Never start a sentence with a symbol. In the last paragraph of page 3, one sentence reads "Distance regular graphs have an intersection array [...] where for any two vertices $v$ and $u$ that are $r$ distance apart, $delta(v,u) = r$." (This seems to be the author's way of defining $delta$, although the phrasing could be better.) The immediately-following $b_r$ is the start of the next sentence, it is not being multiplied by the $r$. Does that help?
– Blue
Aug 29 at 8:19
1
Yes thanks! a silly misunderstanding anyway.
– sachal
Aug 29 at 8:59