Topological properties on the diameters of the integer simplex

Meijie Ma

arXiv:1501.02870·cs.DM·January 15, 2015

Topological properties on the diameters of the integer simplex

Meijie Ma

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TL;DR

This paper determines the wide diameter and fault-diameter of the integer simplex network, showing they are equal to the standard diameter plus one for certain parameters, thus advancing understanding of network robustness.

Contribution

It provides exact formulas for the wide and fault-diameters of the integer simplex, extending previous work on network diameter properties.

Findings

01

Wide and fault-diameters of the integer simplex are equal to the diameter plus one for 2 ≤ ω ≤ n.

02

Results apply to triangular pyramids as special cases of integer simplices.

03

The study enhances understanding of interconnection network robustness and fault tolerance.

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 $2 \leq ω \leq 3$ .

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Taxonomy

TopicsInterconnection Networks and Systems · Carbon Nanotubes in Composites · Supercapacitor Materials and Fabrication