Topological properties on the diameters of the integer simplex

Wide diameter dω(G)dω(G) and fault-diameter Dω(G)Dω(G) of an interconnection network GG have been recently studied by many authors. We determine the wide diameter and fault-diameter of the integer simplex Tmn. Note that d1(Tmn)=D1(Tmn)=d(Tmn), where d(Tmn) is the diameter of Tmn. We prove that dω(Tmn)=Dω(Tmn)=d(Tmn)+1 when 2≤ω≤n2≤ω≤n. Since a triangular pyramid TPLTPL is TL3, we have dω(TPL)=Dω(TPL)=d(TPL)+1dω(TPL)=Dω(TPL)=d(TPL)+1 when 2≤ω≤32≤ω≤3.