Hamiltonian connectivity of 2-tree-generated networks

In this paper we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A n . These graphs are generalizations of the alternating group graph A G n . We look at the case when the 3-cycles form a “tree-like structure”, and analyze the Hamiltonian connectivit...

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Bibliographic Details
Published inMathematical and computer modelling Vol. 48; no. 5; pp. 787 - 804
Main Authors Cheng, Eddie, Lipman, Marc J., Lipták, László, Stiebel, David
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.09.2008
Elsevier Science
Subjects
Alternating group graph
Cayley graph
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Hamiltonian connectivity
Interconnection network
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Sciences and techniques of general use
Interconnection network
Hamiltonian connectivity
Cayley graph
Alternating group graph
Hamiltonian path
Connected graph
Tree structure
Scientific computation
Graph connectivity
Applied mathematics
Mathematical model
Hamiltonian
Computer aided analysis
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Summary:In this paper we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A n . These graphs are generalizations of the alternating group graph A G n . We look at the case when the 3-cycles form a “tree-like structure”, and analyze the Hamiltonian connectivity of such graphs. We prove that even with 2 n − 7 vertices deleted, the remaining graph is Hamiltonian connected, i.e. there is a Hamiltonian path between every pair of vertices.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2007.11.007