A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches
We are thankful to Almighty Allah for His blessings for the successful completion of our thesis. Ourheartiestgratitude,profoundindebtednessanddeeprespectgotooursupervisor, Group Captain Md. Afzal Hossain, psc, Head of the Department, Department of Computer Science and Engineering (CSE), Military Ins...
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| Μορφή: | Thesis |
| Γλώσσα: | Αγγλικά |
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Department of Computer Science and Engineering, Military Institute of Science and Technology
2015
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| Διαθέσιμο Online: | http://hdl.handle.net/123456789/151 |
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| _version_ | 1868227006327422976 |
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| author | Abdul Kader, Mohammad Manjur, Sharmin Manzur Ankon, Md. Tasnim |
| author_browse | Abdul Kader, Mohammad Manjur, Sharmin Manzur Ankon, Md. Tasnim |
| author_facet | Abdul Kader, Mohammad Manjur, Sharmin Manzur Ankon, Md. Tasnim |
| author_sort | Abdul Kader, Mohammad |
| collection | DSpace |
| description | We are thankful to Almighty Allah for His blessings for the successful completion of our thesis. Ourheartiestgratitude,profoundindebtednessanddeeprespectgotooursupervisor, Group Captain Md. Afzal Hossain, psc, Head of the Department, Department of Computer Science and Engineering (CSE), Military Institute of Science and Technology (MIST), for his constant supervision, affectionate guidance and great encouragement and motivation. Hiskeeninterestonthetopicandvaluableadvicesthroughoutthestudywasofgreathelpin completing this thesis. We also thank Lecturer Jannatul Maowa, Department of Computer Science and Engineering (CSE), Military Institute of Science and Technology (MIST), for her relentless guidance and timely advice in completing this thesis work. We are specially grateful to her for introducing us with the topic, as well as for sharing her analytical knowledge and research expertise through out this thesis work.
We are especially grateful to the Department of Computer Science and Engineering (CSE) of Military Institute of Science and Technology (MIST) for providing their all out support during the thesis work.
Finally, we would like to thank our families and our course mates for their appreciable assistance, patience and suggestions during the course of our thesis. |
| format | Thesis |
| id | oai:localhost:123456789-151 |
| institution | My University |
| language | English |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Computer Science and Engineering, Military Institute of Science and Technology |
| publisherStr | Department of Computer Science and Engineering, Military Institute of Science and Technology |
| record_format | dspace |
| spelling | oai:localhost:123456789-1512015-08-04T08:22:31Z A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches Abdul Kader, Mohammad Manjur, Sharmin Manzur Ankon, Md. Tasnim Critical, Assessment, Graceful, Graphs, Trees, Development , Approaches We are thankful to Almighty Allah for His blessings for the successful completion of our thesis. Ourheartiestgratitude,profoundindebtednessanddeeprespectgotooursupervisor, Group Captain Md. Afzal Hossain, psc, Head of the Department, Department of Computer Science and Engineering (CSE), Military Institute of Science and Technology (MIST), for his constant supervision, affectionate guidance and great encouragement and motivation. Hiskeeninterestonthetopicandvaluableadvicesthroughoutthestudywasofgreathelpin completing this thesis. We also thank Lecturer Jannatul Maowa, Department of Computer Science and Engineering (CSE), Military Institute of Science and Technology (MIST), for her relentless guidance and timely advice in completing this thesis work. We are specially grateful to her for introducing us with the topic, as well as for sharing her analytical knowledge and research expertise through out this thesis work. We are especially grateful to the Department of Computer Science and Engineering (CSE) of Military Institute of Science and Technology (MIST) for providing their all out support during the thesis work. Finally, we would like to thank our families and our course mates for their appreciable assistance, patience and suggestions during the course of our thesis. AgraphGisgracefulifitssetofverticesisdenotedbytheset{0,1,...,m}andthe set of edges is denoted by {1,2,...,m}, such that all edges are labeled uniquely and accordingtothedifferenceofthelabelsoftheverticesconnectingit. Asimplenotation to be mentioned that all the vertices will have unique labels, and so will the edges. The idea of graceful labeling came to being from Ringel’s conjecture(see chapter 1). The conjecture introduced in 1963, established the open problem of graceful labeling. Any graphthatcanbelabeledgracefullysuggeststhattheclassofthegraphimpliesRingel’s conjecture. Over the years many people worked on this conjecture and found out many classesofgracefultreesandgraph. SuchgracefulclassesoftreesandgraphsarePathor Chain, Caterpillar, Extended caterpillar, super caterpillar, Star, Olive tree, Banana tree, Lobstar, product tree Cyle wheel, Crown graph etc. A C4 graph is a cycle consisting of four vertices. The C4 graph is graceful. However, graphs formed by multiple number of C4 cycles in them were yet to be studied. Another type of graph is a star. A star S1, nisacentervertexconnectedwithnleaves. Astarisalsoclassifiedasatree,according to the definition. It has been proved earlier that all stars are graceful. The purpose of this paper was to study and develop procedures to gracefully labeled graphs formed by thecombinationofmultiple C4 cyclesandthecombinationofmultiplestars. Ageneral procedure was developed for each of the three classes, proved to be graceful, through thispaper. Furtherresearchwasconductedonfindingmorevarietiesofsuchgraphsand the results were discussed. The result of the research proposes an open problem about aclassofgraphswhichpartiallysupportsRingel’sconjecture. Thepaperhighlightsthe classes of graphs and trees that were previously proved to be graceful. Department of Computer Science and Engineering, Military Institute of Science and Technology 2015-07-05T05:51:55Z 2015-07-05T05:51:55Z 2014-12 Thesis http://hdl.handle.net/123456789/151 en B.Sc. in Computer Science and Engineering Thesis; application/pdf Department of Computer Science and Engineering, Military Institute of Science and Technology |
| spellingShingle | Critical, Assessment, Graceful, Graphs, Trees, Development , Approaches Abdul Kader, Mohammad Manjur, Sharmin Manzur Ankon, Md. Tasnim A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches |
| title | A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches |
| title_full | A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches |
| title_fullStr | A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches |
| title_full_unstemmed | A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches |
| title_short | A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches |
| title_sort | critical assessment of graceful graphs and trees study and development of new approaches |
| topic | Critical, Assessment, Graceful, Graphs, Trees, Development , Approaches |
| url | http://hdl.handle.net/123456789/151 |
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