Coloring binary tree edges with given number of colors
$begingroup$
Let's say I have a balanced binary tree which has 37 leaves.
I can color the vertices of this tree with 37 colors.
$$ 37 * 36^{72} $$ ways.
How can I find out coloring edges with 37 colors?
Original problem is,
1. Let T be a binary tree with 37 leaves.
(b) In how many ways can you color T using 37 colors?
I think the answer for this problem is $$ 37 * 36^{72} $$
I assumed that this value is calculating vertices not edges. So I wondered, how many ways can I color edges of T using 37 colors.
graph-theory trees coloring
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
$endgroup$
|
show 2 more comments
$begingroup$
Let's say I have a balanced binary tree which has 37 leaves.
I can color the vertices of this tree with 37 colors.
$$ 37 * 36^{72} $$ ways.
How can I find out coloring edges with 37 colors?
Original problem is,
1. Let T be a binary tree with 37 leaves.
(b) In how many ways can you color T using 37 colors?
I think the answer for this problem is $$ 37 * 36^{72} $$
I assumed that this value is calculating vertices not edges. So I wondered, how many ways can I color edges of T using 37 colors.
graph-theory trees coloring
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
$endgroup$
$begingroup$
Can you please add a little more explanation?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:02
$begingroup$
@AnkitKumarI did.
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:03
$begingroup$
What does "To color its vertices differently" mean?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:05
$begingroup$
@AnkitKumar I edited
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:07
$begingroup$
I'm sorry, but I'm still unable to understand what it means. If possible, can you tell me where you found this question? Or post a pic of the same?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:08
|
show 2 more comments
$begingroup$
Let's say I have a balanced binary tree which has 37 leaves.
I can color the vertices of this tree with 37 colors.
$$ 37 * 36^{72} $$ ways.
How can I find out coloring edges with 37 colors?
Original problem is,
1. Let T be a binary tree with 37 leaves.
(b) In how many ways can you color T using 37 colors?
I think the answer for this problem is $$ 37 * 36^{72} $$
I assumed that this value is calculating vertices not edges. So I wondered, how many ways can I color edges of T using 37 colors.
graph-theory trees coloring
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
$endgroup$
Let's say I have a balanced binary tree which has 37 leaves.
I can color the vertices of this tree with 37 colors.
$$ 37 * 36^{72} $$ ways.
How can I find out coloring edges with 37 colors?
Original problem is,
1. Let T be a binary tree with 37 leaves.
(b) In how many ways can you color T using 37 colors?
I think the answer for this problem is $$ 37 * 36^{72} $$
I assumed that this value is calculating vertices not edges. So I wondered, how many ways can I color edges of T using 37 colors.
graph-theory trees coloring
graph-theory trees coloring
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
edited Dec 8 '18 at 23:00
Misha Lavrov
46.3k656107
46.3k656107
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
asked Dec 8 '18 at 17:28
jaykodeveloperjaykodeveloper
1238
1238
$begingroup$
Can you please add a little more explanation?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:02
$begingroup$
@AnkitKumarI did.
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:03
$begingroup$
What does "To color its vertices differently" mean?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:05
$begingroup$
@AnkitKumar I edited
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:07
$begingroup$
I'm sorry, but I'm still unable to understand what it means. If possible, can you tell me where you found this question? Or post a pic of the same?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:08
|
show 2 more comments
$begingroup$
Can you please add a little more explanation?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:02
$begingroup$
@AnkitKumarI did.
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:03
$begingroup$
What does "To color its vertices differently" mean?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:05
$begingroup$
@AnkitKumar I edited
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:07
$begingroup$
I'm sorry, but I'm still unable to understand what it means. If possible, can you tell me where you found this question? Or post a pic of the same?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:08
$begingroup$
Can you please add a little more explanation?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:02
$begingroup$
Can you please add a little more explanation?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:02
$begingroup$
@AnkitKumarI did.
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:03
$begingroup$
@AnkitKumarI did.
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:03
$begingroup$
What does "To color its vertices differently" mean?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:05
$begingroup$
What does "To color its vertices differently" mean?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:05
$begingroup$
@AnkitKumar I edited
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:07
$begingroup$
@AnkitKumar I edited
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:07
$begingroup$
I'm sorry, but I'm still unable to understand what it means. If possible, can you tell me where you found this question? Or post a pic of the same?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:08
$begingroup$
I'm sorry, but I'm still unable to understand what it means. If possible, can you tell me where you found this question? Or post a pic of the same?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:08
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Since you've written $37*36^{72}$, I assume you figured out that it has $73$ vertices. Further, no restriction of any kind is given. So, its more of a problem (and a pretty simple one to be honest) on combinatorics and not graph theory.
Coloring vertices- $73$ vertices, each can choose from $37$ colors $implies 37^{73}$ ways!
Coloring edges- $73$ vertices $implies 72$ edges, each can choose from $37$ colors $implies 37^{72}$ ways!
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031380%2fcoloring-binary-tree-edges-with-given-number-of-colors%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Since you've written $37*36^{72}$, I assume you figured out that it has $73$ vertices. Further, no restriction of any kind is given. So, its more of a problem (and a pretty simple one to be honest) on combinatorics and not graph theory.
Coloring vertices- $73$ vertices, each can choose from $37$ colors $implies 37^{73}$ ways!
Coloring edges- $73$ vertices $implies 72$ edges, each can choose from $37$ colors $implies 37^{72}$ ways!
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
$endgroup$
add a comment |
$begingroup$
Since you've written $37*36^{72}$, I assume you figured out that it has $73$ vertices. Further, no restriction of any kind is given. So, its more of a problem (and a pretty simple one to be honest) on combinatorics and not graph theory.
Coloring vertices- $73$ vertices, each can choose from $37$ colors $implies 37^{73}$ ways!
Coloring edges- $73$ vertices $implies 72$ edges, each can choose from $37$ colors $implies 37^{72}$ ways!
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
$endgroup$
add a comment |
$begingroup$
Since you've written $37*36^{72}$, I assume you figured out that it has $73$ vertices. Further, no restriction of any kind is given. So, its more of a problem (and a pretty simple one to be honest) on combinatorics and not graph theory.
Coloring vertices- $73$ vertices, each can choose from $37$ colors $implies 37^{73}$ ways!
Coloring edges- $73$ vertices $implies 72$ edges, each can choose from $37$ colors $implies 37^{72}$ ways!
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
$endgroup$
Since you've written $37*36^{72}$, I assume you figured out that it has $73$ vertices. Further, no restriction of any kind is given. So, its more of a problem (and a pretty simple one to be honest) on combinatorics and not graph theory.
Coloring vertices- $73$ vertices, each can choose from $37$ colors $implies 37^{73}$ ways!
Coloring edges- $73$ vertices $implies 72$ edges, each can choose from $37$ colors $implies 37^{72}$ ways!
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
answered Dec 8 '18 at 18:28
Ankit KumarAnkit Kumar
1,494221
1,494221
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031380%2fcoloring-binary-tree-edges-with-given-number-of-colors%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Can you please add a little more explanation?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:02
$begingroup$
@AnkitKumarI did.
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:03
$begingroup$
What does "To color its vertices differently" mean?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:05
$begingroup$
@AnkitKumar I edited
$endgroup$
– jaykodeveloper
Dec 8 '18 at 18:07
$begingroup$
I'm sorry, but I'm still unable to understand what it means. If possible, can you tell me where you found this question? Or post a pic of the same?
$endgroup$
– Ankit Kumar
Dec 8 '18 at 18:08