Pancyclicity of ternary n-cube networks under the conditional fault model

A graph G is said to be conditional k-edge-fault pancyclic if after removing k faulty edges from G  , under the assumption that each vertex is incident to at least two fault-free edges, the resulting graph contains a cycle of every length from its girth to |V(G)||V(G)|. In this paper, we consider ternary n  -cube networks and show that they are conditional (4n−5)(4n−5)-edge-fault pancyclic.

Research highlights► We investigate the pancyclicity of ternary n-cube networks under the conditional fault model. ► We give the upper bound on the number of faulty edges that the ternary n-cube network can tolerant. ► No more faulty edges can be added in order to keep the pancyclicity.