Hamilton-connectedness and Hamilton-laceability of planar geometric graphs with applications

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 no...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 4; pp. 3947 - 3973
Main Authors Khan, Suliman, Hayat, Sakander, Khan, Asad, Malik, Muhammad Yasir Hayat, Cao, Jinde
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
convex polytopes
detour index
graph
hamilton-connected graph
hamiltonian cycle
hamiltonian path
np-complete problems
platonic solids
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021235

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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021235