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Fault-tolerant edge and vertex pancyclicity in alternating group graphs

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
217
Issue
6
Identifiers
DOI: 10.1016/j.amc.2010.08.018
Keywords
  • Hamiltonian Cycle
  • Pancyclicity
  • Alternating Group Graph
  • Fault Tolerance

Abstract

Abstract In [J.-M. Chang, J.-S. Yang. Fault-tolerant cycle-embedding in alternating group graphs, Appl. Math. Comput. 197 (2008) 760–767] the authors claim that every alternating group graph AG n is ( n − 4)-fault-tolerant edge 4-pancyclic. Which means that if the number of faults ∣ F∣ ⩽ n − 4, then every edge in AG n − F is contained in a cycle of length ℓ, for every 4 ⩽ ℓ ⩽ n!/2 − ∣ F∣. They also claim that AG n is ( n − 3)-fault-tolerant vertex pancyclic. Which means that if ∣ F∣ ⩽ n − 3, then every vertex in AG n − F is contained in a cycle of length ℓ, for every 3 ⩽ ℓ ⩽ n!/2 − ∣ F∣. Their proofs are not complete. They left a few important things unexplained. In this paper we fulfill these gaps and present another proofs that AG n is ( n − 4)-fault-tolerant edge 4-pancyclic and ( n − 3)-fault-tolerant vertex pancyclic.

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