Can a tree graph have only one vertex? And if so, that means that a tree graph has at minimum one leaf?
1
$begingroup$
Also, if the tree is two vertices connected by an edge, does the root count as a leaf too? Since it's also a vertex of degree one?
I've had trouble clarifying this online and from my textbook. Thank you.
discrete-mathematics trees
asked Dec 16 '18 at 20:24
JLotusJLotus
63
$endgroup$
add a comment |
1
$begingroup$
Also, if the tree is two vertices connected by an edge, does the root count as a leaf too? Since it's also a vertex of degree one?
I've had trouble clarifying this online and from my textbook. Thank you.
discrete-mathematics trees
asked Dec 16 '18 at 20:24
JLotusJLotus
63
$endgroup$
add a comment |
1
1
1
$begingroup$
Also, if the tree is two vertices connected by an edge, does the root count as a leaf too? Since it's also a vertex of degree one?
I've had trouble clarifying this online and from my textbook. Thank you.
discrete-mathematics trees
asked Dec 16 '18 at 20:24
JLotusJLotus
63
$endgroup$
Also, if the tree is two vertices connected by an edge, does the root count as a leaf too? Since it's also a vertex of degree one?
I've had trouble clarifying this online and from my textbook. Thank you.
discrete-mathematics trees
discrete-mathematics trees
asked Dec 16 '18 at 20:24
JLotusJLotus
63
asked Dec 16 '18 at 20:24
JLotusJLotus
63
edited Dec 16 '18 at 20:34
JLotus
asked Dec 16 '18 at 20:24
JLotusJLotus
63
asked Dec 16 '18 at 20:24
JLotusJLotus
63
asked Dec 16 '18 at 20:24
JLotusJLotus
63
63
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
0
$begingroup$
For the former: yes, by most definitions, the one-vertex, zero-edge graph is a tree.
For the latter: yes, all vertices of degree 1 are leaves. In general, which node you call the "root" is pretty much arbitrary.
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
$endgroup$
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
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
});
}
});
draft saved
draft discarded
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%2f3043113%2fcan-a-tree-graph-have-only-one-vertex-and-if-so-that-means-that-a-tree-graph-h%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
0
$begingroup$
For the former: yes, by most definitions, the one-vertex, zero-edge graph is a tree.
For the latter: yes, all vertices of degree 1 are leaves. In general, which node you call the "root" is pretty much arbitrary.
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
$endgroup$
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
add a comment |
0
$begingroup$
For the former: yes, by most definitions, the one-vertex, zero-edge graph is a tree.
For the latter: yes, all vertices of degree 1 are leaves. In general, which node you call the "root" is pretty much arbitrary.
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
$endgroup$
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
add a comment |
0
0
0
$begingroup$
For the former: yes, by most definitions, the one-vertex, zero-edge graph is a tree.
For the latter: yes, all vertices of degree 1 are leaves. In general, which node you call the "root" is pretty much arbitrary.
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
$endgroup$
For the former: yes, by most definitions, the one-vertex, zero-edge graph is a tree.
For the latter: yes, all vertices of degree 1 are leaves. In general, which node you call the "root" is pretty much arbitrary.
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
edited Jan 22 at 11:17
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
answered Dec 16 '18 at 20:28
user3482749user3482749
4,266919
4,266919
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
add a comment |
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
Ok thank you. My teacher wrote in her notes that it has at minimum one leaf and then wrote that it has two minimum elsewhere. Perhaps she meant to say one leaf minimum for our purposes.
$endgroup$
– JLotus
Dec 16 '18 at 20:32
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user3482749 it seems to me that OP meant in the second part a graph containing just 2 vertices connected by 1 edge: the tree is two vertices connected by an edge. Can you revise your answer in this sense?
$endgroup$
– user376343
Jan 21 at 20:38
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user376343 Ah, that's been edited since I answered. With that version, yes, that's a tree.
$endgroup$
– user3482749
Jan 21 at 21:05
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
$begingroup$
@user3482749 I would gladly upvote your answer but as it is, is not fully coherent.
$endgroup$
– user376343
Jan 21 at 21:53
add a comment |
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3043113%2fcan-a-tree-graph-have-only-one-vertex-and-if-so-that-means-that-a-tree-graph-h%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
