Pelabelan graceful dan pelabelan ̂, pada graf pot bunga dan graf pohon palem = Graceful labeling and ̂, labeling of flower pot graph and palm tree graph
| Main Authors: | Muzayyin Ahmad, author, Add author: Kiki Ariyanti Sugeng, supervisor, Add author: Silaban, Denny Riama, supervisor, Add author: Hendri Mufti, examiner, Add author: Hengki Tasman, examiner, Add author: Siti Aminah, examiner |
|---|---|
| Format: | Masters Doctoral |
| Terbitan: |
, 2012
|
| Subjects: | |
| Online Access: |
https://lib.ui.ac.id/detail?id=20298575 |
| ctrlnum |
20298575 |
|---|---|
| fullrecord |
<?xml version="1.0"?>
<dc schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><type>Thesis:Masters</type><title>Pelabelan graceful dan pelabelan &#770;, pada graf pot bunga dan graf pohon palem = Graceful labeling and &#770;, labeling of flower pot graph and palm tree graph</title><creator>Muzayyin Ahmad, author</creator><creator>Add author: Kiki Ariyanti Sugeng, supervisor</creator><creator>Add author: Silaban, Denny Riama, supervisor</creator><creator>Add author: Hendri Mufti, examiner</creator><creator>Add author: Hengki Tasman, examiner</creator><creator>Add author: Siti Aminah, examiner</creator><publisher/><date>2012</date><subject>Calculus.</subject><description>[<b>ABSTRAK</b><br>
Pelabelan pada graf G adalah penetapan nilai bilangan bulat untuk simpul dan busur dari G dengan aturan tertentu. Pelabelan graceful adalah fungsi injektif g dari himpunan simpul V ke himpunan bilangan { | |} yang menginduksi fungsi bijektif g? dari himpunan busur E ke himpunan bilangan { | |}, dimana setiap busur uv E dengan simpul u,v V berlaku g?(uv) = |g(u) ? g(v)|. Pelabelan &#770; merupakan modifikasi lain dari pelabelan graceful. Pelabelan &#770; adalah fungsi injektif h dari himpunan simpul V ke himpunan bilangan { | | } yang menginduksi fungsi bijektif h? dari himpunan busur E ke himpunan bilangan { | |} atau { | | | | }, dimana setiap busur uv E dengan simpul u,v V berlaku h?(uv) =| ? |. Graf pot bunga ( ) dibentuk dari gabungan graf bintang dan graf lingkaran dengan tambahan busur yang menghubungkan pusat graf bintang dengan salah satu simpul pada graf lingkaran . Graf pohon palem ( ) merupakan gabungan graf sapu dan graf lingkaran dengan tambahan busur yang menghubungkan simpul ujung graf dengan salah satu simpul pada graf lingkaran . Pada makalah ini diberikan konstruksi pelabelan graceful dan pelabelan &#770; untuk graf pot bunga ( ) dan graf pohon palem ( ), dengan k bilangan bulat, k &#8805; 3 dan m, n bilangan asli. Pelabelan graceful pada graf pot bunga dan graf pohon palem hanya untuk k &#8801; 0, 3 (mod 4).
<hr>
<b>Abstract</b><br>
A labeling on a graph G is an asingment of integer value to vertex and edge of G with certain rule. A graceful labeling is an injective function g from the set of vertices V to a set of numbers {0,1,2,?, |E|} which induces a bijective function g' from the set E to the set of numbers {1,2,?,|E|}, where for each edge uv E with u, v V applies g?(uv) = |g(u) ? g(v)|. A &#770; labeling is a modification of graceful labeling. The &#770; labeling is an injective function h from the set V to the set of numbers {0,1,2,?,|E|+1} which induces a bijective function h' from the set of edges E to the set of numbers {1,2,?,|E|} or {1,2,?,|E|-1, |E|+1}, where each edge u v E with u, v V applies h? (u v) = | ? |. A flower pot graph ( ) is formed by combining the center of star graph with a vertex of cycle graph with an edge. A palm tree graph ( ) is formed by combining the end vertex of broom graph with a vertex of cycle . In this thesis is given constructions of graceful labeling and &#770; labeling for flower pot graph ( ) and palm tree graph ( ), with integer k &#8805; 3 and m, n are positive integer. Graceful labeling on flower pot graph and palm tree graph are given only for k &#8801; 0, 3 (mod 4).;A labeling on a graph G is an asingment of integer value to vertex and edge of G with certain rule. A graceful labeling is an injective function g from the set of vertices V to a set of numbers {0,1,2,?, |E|} which induces a bijective function g' from the set E to the set of numbers {1,2,?,|E|}, where for each edge uv E with u, v V applies g?(uv) = |g(u) ? g(v)|. A &#770; labeling is a modification of graceful labeling. The &#770; labeling is an injective function h from the set V to the set of numbers {0,1,2,?,|E|+1} which induces a bijective function h' from the set of edges E to the set of numbers {1,2,?,|E|} or {1,2,?,|E|-1, |E|+1}, where each edge u v E with u, v V applies h? (u v) = | ? |. A flower pot graph ( ) is formed by combining the center of star graph with a vertex of cycle graph with an edge. A palm tree graph ( ) is formed by combining the end vertex of broom graph with a vertex of cycle . In this thesis is given constructions of graceful labeling and &#770; labeling for flower pot graph ( ) and palm tree graph ( ), with integer k &#8805; 3 and m, n are positive integer. Graceful labeling on flower pot graph and palm tree graph are given only for k &#8801; 0, 3 (mod 4)., A labeling on a graph G is an asingment of integer value to vertex and edge of G with certain rule. A graceful labeling is an injective function g from the set of vertices V to a set of numbers {0,1,2,?, |E|} which induces a bijective function g' from the set E to the set of numbers {1,2,?,|E|}, where for each edge uv E with u, v V applies g?(uv) = |g(u) ? g(v)|. A &#770; labeling is a modification of graceful labeling. The &#770; labeling is an injective function h from the set V to the set of numbers {0,1,2,?,|E|+1} which induces a bijective function h' from the set of edges E to the set of numbers {1,2,?,|E|} or {1,2,?,|E|-1, |E|+1}, where each edge u v E with u, v V applies h? (u v) = | ? |. A flower pot graph ( ) is formed by combining the center of star graph with a vertex of cycle graph with an edge. A palm tree graph ( ) is formed by combining the end vertex of broom graph with a vertex of cycle . In this thesis is given constructions of graceful labeling and &#770; labeling for flower pot graph ( ) and palm tree graph ( ), with integer k &#8805; 3 and m, n are positive integer. Graceful labeling on flower pot graph and palm tree graph are given only for k &#8801; 0, 3 (mod 4).]</description><identifier>https://lib.ui.ac.id/detail?id=20298575</identifier><recordID>20298575</recordID></dc>
|
| format |
Thesis:Masters Thesis Thesis:Doctoral |
| author |
Muzayyin Ahmad, author Add author: Kiki Ariyanti Sugeng, supervisor Add author: Silaban, Denny Riama, supervisor Add author: Hendri Mufti, examiner Add author: Hengki Tasman, examiner Add author: Siti Aminah, examiner |
| title |
Pelabelan graceful dan pelabelan ̂, pada graf pot bunga dan graf pohon palem = Graceful labeling and ̂, labeling of flower pot graph and palm tree graph |
| publishDate |
2012 |
| topic |
Calculus |
| url |
https://lib.ui.ac.id/detail?id=20298575 |
| contents |
[<b>ABSTRAK</b><br>
Pelabelan pada graf G adalah penetapan nilai bilangan bulat untuk simpul dan busur dari G dengan aturan tertentu. Pelabelan graceful adalah fungsi injektif g dari himpunan simpul V ke himpunan bilangan { | |} yang menginduksi fungsi bijektif g? dari himpunan busur E ke himpunan bilangan { | |}, dimana setiap busur uv E dengan simpul u,v V berlaku g?(uv) = |g(u) ? g(v)|. Pelabelan ̂ merupakan modifikasi lain dari pelabelan graceful. Pelabelan ̂ adalah fungsi injektif h dari himpunan simpul V ke himpunan bilangan { | | } yang menginduksi fungsi bijektif h? dari himpunan busur E ke himpunan bilangan { | |} atau { | | | | }, dimana setiap busur uv E dengan simpul u,v V berlaku h?(uv) =| ? |. Graf pot bunga ( ) dibentuk dari gabungan graf bintang dan graf lingkaran dengan tambahan busur yang menghubungkan pusat graf bintang dengan salah satu simpul pada graf lingkaran . Graf pohon palem ( ) merupakan gabungan graf sapu dan graf lingkaran dengan tambahan busur yang menghubungkan simpul ujung graf dengan salah satu simpul pada graf lingkaran . Pada makalah ini diberikan konstruksi pelabelan graceful dan pelabelan ̂ untuk graf pot bunga ( ) dan graf pohon palem ( ), dengan k bilangan bulat, k ≥ 3 dan m, n bilangan asli. Pelabelan graceful pada graf pot bunga dan graf pohon palem hanya untuk k ≡ 0, 3 (mod 4).
<hr>
<b>Abstract</b><br>
A labeling on a graph G is an asingment of integer value to vertex and edge of G with certain rule. A graceful labeling is an injective function g from the set of vertices V to a set of numbers {0,1,2,?, |E|} which induces a bijective function g' from the set E to the set of numbers {1,2,?,|E|}, where for each edge uv E with u, v V applies g?(uv) = |g(u) ? g(v)|. A ̂ labeling is a modification of graceful labeling. The ̂ labeling is an injective function h from the set V to the set of numbers {0,1,2,?,|E|+1} which induces a bijective function h' from the set of edges E to the set of numbers {1,2,?,|E|} or {1,2,?,|E|-1, |E|+1}, where each edge u v E with u, v V applies h? (u v) = | ? |. A flower pot graph ( ) is formed by combining the center of star graph with a vertex of cycle graph with an edge. A palm tree graph ( ) is formed by combining the end vertex of broom graph with a vertex of cycle . In this thesis is given constructions of graceful labeling and ̂ labeling for flower pot graph ( ) and palm tree graph ( ), with integer k ≥ 3 and m, n are positive integer. Graceful labeling on flower pot graph and palm tree graph are given only for k ≡ 0, 3 (mod 4).;A labeling on a graph G is an asingment of integer value to vertex and edge of G with certain rule. A graceful labeling is an injective function g from the set of vertices V to a set of numbers {0,1,2,?, |E|} which induces a bijective function g' from the set E to the set of numbers {1,2,?,|E|}, where for each edge uv E with u, v V applies g?(uv) = |g(u) ? g(v)|. A ̂ labeling is a modification of graceful labeling. The ̂ labeling is an injective function h from the set V to the set of numbers {0,1,2,?,|E|+1} which induces a bijective function h' from the set of edges E to the set of numbers {1,2,?,|E|} or {1,2,?,|E|-1, |E|+1}, where each edge u v E with u, v V applies h? (u v) = | ? |. A flower pot graph ( ) is formed by combining the center of star graph with a vertex of cycle graph with an edge. A palm tree graph ( ) is formed by combining the end vertex of broom graph with a vertex of cycle . In this thesis is given constructions of graceful labeling and ̂ labeling for flower pot graph ( ) and palm tree graph ( ), with integer k ≥ 3 and m, n are positive integer. Graceful labeling on flower pot graph and palm tree graph are given only for k ≡ 0, 3 (mod 4)., A labeling on a graph G is an asingment of integer value to vertex and edge of G with certain rule. A graceful labeling is an injective function g from the set of vertices V to a set of numbers {0,1,2,?, |E|} which induces a bijective function g' from the set E to the set of numbers {1,2,?,|E|}, where for each edge uv E with u, v V applies g?(uv) = |g(u) ? g(v)|. A ̂ labeling is a modification of graceful labeling. The ̂ labeling is an injective function h from the set V to the set of numbers {0,1,2,?,|E|+1} which induces a bijective function h' from the set of edges E to the set of numbers {1,2,?,|E|} or {1,2,?,|E|-1, |E|+1}, where each edge u v E with u, v V applies h? (u v) = | ? |. A flower pot graph ( ) is formed by combining the center of star graph with a vertex of cycle graph with an edge. A palm tree graph ( ) is formed by combining the end vertex of broom graph with a vertex of cycle . In this thesis is given constructions of graceful labeling and ̂ labeling for flower pot graph ( ) and palm tree graph ( ), with integer k ≥ 3 and m, n are positive integer. Graceful labeling on flower pot graph and palm tree graph are given only for k ≡ 0, 3 (mod 4).] |
| id |
IOS18068.20298575 |
| institution |
Universitas Indonesia |
| institution_id |
51 |
| institution_type |
library:university library |
| library |
Perpustakaan Universitas Indonesia |
| library_id |
492 |
| collection |
Repository Disertasi (Membership) Universitas Indonesia |
| repository_id |
18068 |
| city |
KOTA DEPOK |
| province |
JAWA BARAT |
| repoId |
IOS18068 |
| first_indexed |
2022-12-14T04:11:14Z |
| last_indexed |
2022-12-14T04:11:14Z |
| recordtype |
dc |
| merged_child_boolean |
1 |
| _version_ |
1752197474247770112 |
| score |
17.610468 |