The Hamilton spaces of Cayley graphs on abelian groups
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The Hamilton space of any connected Cayley graph on an abelian group is determined in this paper and is shown to be a subspace of the cycle space called the Hamilton space.About:
This article is published in Discrete Mathematics.The article was published on 1990-06-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Cayley graph & Vertex-transitive graph.read more
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Hamilton cycles and paths in vertex-transitive graphs-Current directions
Klavdija Kutnar,Dragan Marušič +1 more
TL;DR: Current directions in solving Lovasz's problem about the existence of Hamilton cycles and paths in connected vertex-transitive graphs are given.
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Generalized Cayley graphs
TL;DR: The concept of generalized Cayley graphs is introduced and their properties are studied, in particular relative to double coverings of graphs.
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Hamiltonicity of cubic Cayley graphs
Henry H. Glover,Dragan Marušič +1 more
TL;DR: In this paper it was shown that Cayley graphs arising from finite groups having a $(2,s,3)$-presentation have a Hamilton cycle for any finite connected vertex-transitive graph.
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Hamiltonicity of Cubic Cayley Graphs
Henry H. Glover,Dragan Marušič +1 more
TL;DR: In this article, it was shown that Cayley graphs arising from groups having a $(2,s,3)$-presentation have a Hamilton cycle when the group is congruent to 2 modulo 4 and has a long cycle missing only two vertices.
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Hamiltonicity of vertex-transitive graphs of order 4p
Klavdija Kutnar,Dragan Marušič +1 more
TL;DR: It is shown that every connected vertex-transitive graph of order 4p, where p is a prime, is hamiltonian with the exception of the Coxeter graph which is known to possess a Hamilton path.
References
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Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird
Book
Graphs, Groups and Surfaces
TL;DR: In this paper, the Cayley Color Graph of a Group of Graphs is presented as an example of a graph automorphism group, which is a group of graph automata.
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In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen†
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Algorithms for Generating Fundamental Cycles in a Graph
TL;DR: It is shown that for regular graphs of order n the expected value of the total length of a minimum fundamentalcycle set does not exceed O(n2).