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Hamilton-connectedness and Hamilton-laceability of planar geometric graphs with applications
- Source :
- AIMS Mathematics, Vol 6, Iss 4, Pp 3947-3973 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- In this paper, we have used two different proof techniques to show the Hamilton-connectedness of graphs. By using the vertex connectivity and Hamiltoniancity of graphs, we construct an infinite family of Hamilton-connected convex polytope line graphs whose underlying family of convex polytopes is not Hamilton-connected. By definition, we constructed two more infinite families of Hamilton-connected convex polytopes. As a by-product of our results, we compute exact values of the detour index of the families of Hamilton-connected convex polytopes. Finally, we classify the Platonic solids according to their Hamilton-connectedness and Hamilton-laceability properties.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 4
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.7c9b09f3d64d4def9bed7762e1ba6e18
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.2021235?viewType=HTML