How many different spanning trees can be created from 3 spanning trees?
$begingroup$
We have 3 spanning trees. First consisting of 2 vertices, second from 1 vertice and third from 1 vertice. Total number of nodes in the graph is 4. We have to connect these three spanning trees to form one. On how many different ways we can do this. I know we have to use Cayley's Formula but I do not know how
example: 4 {1} {2} Returns: 8 There are eight spanning trees that contain the edge (1, 2): {(1, 2), (1, 3), (1, 4)} {(1, 2), (1, 3), (2, 4)} {(1, 2), (1, 3), (3, 4)} {(1, 2), (2, 3), (2, 4)} {(1, 2), (1, 4), (2, 3)} {(1, 2), (1, 4), (3, 4)} {(1, 2), (2, 3), (3, 4)} {(1, 2), (2, 4), (3, 4)} We have 4 vertices, two of them are already connected (1,2) and 3 and 4 are disconnected. we need to connect 3 and 4 to (1,2). I need an explanation of this formula: (n)^(k – 2) * s_0 * s_1 * … * s_{k-1} which confirms the above example n-number of vertices k-connected component
graph-theory
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
$endgroup$
add a comment |
$begingroup$
We have 3 spanning trees. First consisting of 2 vertices, second from 1 vertice and third from 1 vertice. Total number of nodes in the graph is 4. We have to connect these three spanning trees to form one. On how many different ways we can do this. I know we have to use Cayley's Formula but I do not know how
example: 4 {1} {2} Returns: 8 There are eight spanning trees that contain the edge (1, 2): {(1, 2), (1, 3), (1, 4)} {(1, 2), (1, 3), (2, 4)} {(1, 2), (1, 3), (3, 4)} {(1, 2), (2, 3), (2, 4)} {(1, 2), (1, 4), (2, 3)} {(1, 2), (1, 4), (3, 4)} {(1, 2), (2, 3), (3, 4)} {(1, 2), (2, 4), (3, 4)} We have 4 vertices, two of them are already connected (1,2) and 3 and 4 are disconnected. we need to connect 3 and 4 to (1,2). I need an explanation of this formula: (n)^(k – 2) * s_0 * s_1 * … * s_{k-1} which confirms the above example n-number of vertices k-connected component
graph-theory
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
$endgroup$
1
$begingroup$
All spanning trees of a graph have the same number of vertices. It is unclear to me what you are trying to ask.
$endgroup$
– Leen Droogendijk
Jan 13 at 13:55
$begingroup$
You should clearly state your problem. Are they 3 spanning trees from the same graph? If not, there are just tree aren't they? And a "tree" on 1 vertex is only an isolated vertex... What do you want to do?
$endgroup$
– Thomas Lesgourgues
Jan 13 at 16:07
add a comment |
$begingroup$
We have 3 spanning trees. First consisting of 2 vertices, second from 1 vertice and third from 1 vertice. Total number of nodes in the graph is 4. We have to connect these three spanning trees to form one. On how many different ways we can do this. I know we have to use Cayley's Formula but I do not know how
example: 4 {1} {2} Returns: 8 There are eight spanning trees that contain the edge (1, 2): {(1, 2), (1, 3), (1, 4)} {(1, 2), (1, 3), (2, 4)} {(1, 2), (1, 3), (3, 4)} {(1, 2), (2, 3), (2, 4)} {(1, 2), (1, 4), (2, 3)} {(1, 2), (1, 4), (3, 4)} {(1, 2), (2, 3), (3, 4)} {(1, 2), (2, 4), (3, 4)} We have 4 vertices, two of them are already connected (1,2) and 3 and 4 are disconnected. we need to connect 3 and 4 to (1,2). I need an explanation of this formula: (n)^(k – 2) * s_0 * s_1 * … * s_{k-1} which confirms the above example n-number of vertices k-connected component
graph-theory
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
$endgroup$
We have 3 spanning trees. First consisting of 2 vertices, second from 1 vertice and third from 1 vertice. Total number of nodes in the graph is 4. We have to connect these three spanning trees to form one. On how many different ways we can do this. I know we have to use Cayley's Formula but I do not know how
example: 4 {1} {2} Returns: 8 There are eight spanning trees that contain the edge (1, 2): {(1, 2), (1, 3), (1, 4)} {(1, 2), (1, 3), (2, 4)} {(1, 2), (1, 3), (3, 4)} {(1, 2), (2, 3), (2, 4)} {(1, 2), (1, 4), (2, 3)} {(1, 2), (1, 4), (3, 4)} {(1, 2), (2, 3), (3, 4)} {(1, 2), (2, 4), (3, 4)} We have 4 vertices, two of them are already connected (1,2) and 3 and 4 are disconnected. we need to connect 3 and 4 to (1,2). I need an explanation of this formula: (n)^(k – 2) * s_0 * s_1 * … * s_{k-1} which confirms the above example n-number of vertices k-connected component
graph-theory
graph-theory
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
edited Jan 16 at 16:12
Kristian Čotić
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
asked Jan 13 at 11:46
Kristian ČotićKristian Čotić
12
12
1
$begingroup$
All spanning trees of a graph have the same number of vertices. It is unclear to me what you are trying to ask.
$endgroup$
– Leen Droogendijk
Jan 13 at 13:55
$begingroup$
You should clearly state your problem. Are they 3 spanning trees from the same graph? If not, there are just tree aren't they? And a "tree" on 1 vertex is only an isolated vertex... What do you want to do?
$endgroup$
– Thomas Lesgourgues
Jan 13 at 16:07
add a comment |
1
$begingroup$
All spanning trees of a graph have the same number of vertices. It is unclear to me what you are trying to ask.
$endgroup$
– Leen Droogendijk
Jan 13 at 13:55
$begingroup$
You should clearly state your problem. Are they 3 spanning trees from the same graph? If not, there are just tree aren't they? And a "tree" on 1 vertex is only an isolated vertex... What do you want to do?
$endgroup$
– Thomas Lesgourgues
Jan 13 at 16:07
1
1
$begingroup$
All spanning trees of a graph have the same number of vertices. It is unclear to me what you are trying to ask.
$endgroup$
– Leen Droogendijk
Jan 13 at 13:55
$begingroup$
All spanning trees of a graph have the same number of vertices. It is unclear to me what you are trying to ask.
$endgroup$
– Leen Droogendijk
Jan 13 at 13:55
$begingroup$
You should clearly state your problem. Are they 3 spanning trees from the same graph? If not, there are just tree aren't they? And a "tree" on 1 vertex is only an isolated vertex... What do you want to do?
$endgroup$
– Thomas Lesgourgues
Jan 13 at 16:07
$begingroup$
You should clearly state your problem. Are they 3 spanning trees from the same graph? If not, there are just tree aren't they? And a "tree" on 1 vertex is only an isolated vertex... What do you want to do?
$endgroup$
– Thomas Lesgourgues
Jan 13 at 16:07
add a comment |
0
active
oldest
votes
Your Answer
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%2f3071925%2fhow-many-different-spanning-trees-can-be-created-from-3-spanning-trees%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3071925%2fhow-many-different-spanning-trees-can-be-created-from-3-spanning-trees%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
1
$begingroup$
All spanning trees of a graph have the same number of vertices. It is unclear to me what you are trying to ask.
$endgroup$
– Leen Droogendijk
Jan 13 at 13:55
$begingroup$
You should clearly state your problem. Are they 3 spanning trees from the same graph? If not, there are just tree aren't they? And a "tree" on 1 vertex is only an isolated vertex... What do you want to do?
$endgroup$
– Thomas Lesgourgues
Jan 13 at 16:07