Hamiltonicity of certain vertex symmetric graphs
Date
1992
Authors
Jiang, Ming
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Abstract
Vertex symmetric graphs play an important role in the design of parallel architectures. In this thesis, we study Hamiltonicity in specific families of Cayley graphs and vertex symmetric graphs. In the first part of the thesis, we study the Hamiltonicity in Faber-Moore digraphs. Faber-Moore digraphs have been proposed as a method of efficient parallel architectures in which information flows unidirectionally. We prove that every Faber-Moore digraph is Hamiltonian. In addition, we give a sufficient and necessary condition for the existence of Hamilton path between any pair of vertices. In the second part of the thesis, we give an efficient algorithm to generate permutations by a tree of transpositions. This algorithm finds Hamilton paths in the corresponding tree Cayley graphs. We give some open problems in the last part of the thesis.
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UN SDG 11: Sustainable Cities and Communities