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2009•Algebra ColloquiumRequires access

Two Sufficient Conditions for Vertex-transitive Hamilton Graphs of Prime-power Order

Cui Zhang, Jiangtao Shi, Wujie Shi

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Abstract

A Hamilton cycle in a graph is a cycle going through all vertices of the graph, and a graph is said to be a Hamilton graph if it has a Hamilton cycle. In this article, two sufficient conditions for vertex-transitive Hamilton graphs of prime-power order are given. Using these conditions, two infinite families of Hamilton graphs of order a 2-power are constructed.

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What this paper is about

A Hamilton cycle in a graph is a cycle going through all vertices of the graph, and a graph is said to be a Hamilton graph if it has a Hamilton cycle. In this article, two sufficient conditions for vertex-transitive Hamilton graphs of prime-power order are given. Using these conditions, two infinite families of Hamilton graphs of order a 2-power are constructed.

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Available abstract

A Hamilton cycle in a graph is a cycle going through all vertices of the graph, and a graph is said to be a Hamilton graph if it has a Hamilton cycle. In this article, two sufficient conditions for vertex-transitive Hamilton graphs of prime-power order are given. Using these conditions, two infinite families of Hamilton graphs of order a 2-power are constructed.

Key concepts: Mathematics, Combinatorics, Discrete mathematics, Hamiltonian path, Vertex (graph theory), Circulant graph, Transitive relation, Symmetric graph

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