Topological properties on the diameters of the integer simplex

Meijie Ma

paper

Topological properties on the diameters of the integer simplex

arXiv:1501.02870

Abstract

Wide diameter $d_{ω} (G)$ and fault-diameter $D_{ω} (G)$ of an interconnection network $G$ have been recently studied by many authors. We determine the wide diameter and fault-diameter of the integer simplex $T_{m}^{n}$ . Note that $d_{1} (T_{m}^{n}) = D_{1} (T_{m}^{n}) = d (T_{m}^{n})$ , where $d (T_{m}^{n})$ is the diameter of $T_{m}^{n}$ . We prove that $d_{ω} (T_{m}^{n}) = D_{ω} (T_{m}^{n}) = d (T_{m}^{n}) + 1$ when $2 \leq ω \leq n$ . Since a triangular pyramid $T P_{L}$ is $T_{L}^{3}$ , we have $d_{ω} (T P_{L}) = D_{ω} (T P_{L}) = d (T P_{L}) + 1$ when $2 \leq ω \leq 3$ .