Edge-Colored Graphs with Applications To Homogeneous Faults

TL;DR

This paper models network faults using edge-colored graphs to determine minimal connectivity requirements for robustness against homogeneous faults, providing conditions for various fault scenarios.

Contribution

It introduces a graph-theoretic model for homogeneous network faults and derives necessary and sufficient conditions for network robustness in key cases.

Findings

Derived conditions for network robustness against homogeneous faults.

Identified minimal connectivity thresholds for different fault scenarios.

Analyzed cases with limited device types and fault thresholds.

Abstract

In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults within certain thresholds. In particular, necessary and sufficient conditions for most interesting cases are obtained. For example, we will study the following cases: (1) the number of colors (or the number of non-homogeneous network device types) is one more than the homogeneous fault threshold; (2) there is only one homogeneous fault (i.e., only one color could fail); and (3) the number of non-homogeneous network device types is less than five.