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DC Field | Value | Language |
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dc.contributor.author | Withanaarachchi, W.A.K.D.H. | - |
dc.contributor.author | Almeida, S.V.A. | - |
dc.contributor.author | Wijesiri, G.S. | - |
dc.date.accessioned | 2024-01-09T09:07:28Z | - |
dc.date.available | 2024-01-09T09:07:28Z | - |
dc.date.issued | 2023 | - |
dc.identifier.citation | Withanaarachchi W.A.K.D.H.; Almeida S.V.A.; Wijesiri G.S. (2023), Maximal embedding genus of 3-edge connected harary graphs, proceedings of the postgraduate institute of Science Research Congress, postgraduate institute of Science Research Congress, Sri Lanka, | en_US |
dc.identifier.uri | http://repository.kln.ac.lk/handle/123456789/27173 | - |
dc.description.abstract | One of the most prominent problems of topological graph theory is to determine the type of surface a nonplanar graph can be embedded. Almost complete results have been obtained for 4-edge connected graphs. The methods that were used to obtain specific results (finding the maximum and minimum genus embedding) for 4-edge connected graphs do not generalise for 3-edge connected graphs. Graph embedding is an important representational technique that aims to maintain the structure of a graph while learning low-dimensional representations of its vertices. The aim of this research project was to study the embedding of 3-edge connected Harary graphs H3,n. Specifically to complete the problem of maximal embeddings of 3-edge connected Harary graphs. The result is proved using Jungerman’s study, which showed that for any graph, is upper-embeddable if and only if it has a spanning tree T such that has at most one component with an odd number of edges. More specifically, a spanning tree for each graph was observed by dividing all 3-edge connected Harary graphs into two groups: odd number of vertices and even number of vertices. The pattern of a set of deleting edges and corresponding spanning trees was generalised in both cases. It was proved that H3,n is upper-embeddable, and the maximum genus of H3,n is given by for each n, by analysing the odd components of the complement of the corresponding spanning trees. | en_US |
dc.publisher | Faculty of Science, University of Kelaniya Sri Lanka | en_US |
dc.subject | 3-Edge connected graphs, Harary graph, Spanning tree, Upper-embeddability | en_US |
dc.title | Maximal embedding genus of 3-edge connected harary graphs | en_US |
Appears in Collections: | Mathematics |
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