Graph Coloring as a Measure of Network Vulnerability

TL;DR

This paper introduces new graph coloring-based parameters to measure network vulnerability, analyzing how failures affect network operability by examining chromatic numbers under various failure scenarios.

Contribution

It proposes novel parameters related to graph coloring to quantify network vulnerability and analyzes their behavior under different failure types and graph structures.

Findings

Minimum k-chromatic number indicates failure thresholds for network inoperability.

Edge, vertex, and mixed failures impact network chromatic properties differently.

Results vary across paths, cycles, and complete graphs, highlighting structural vulnerabilities.

Abstract

We consider new parameters for conditional network vulnerability related to graph coloring. We define a network to be in operation if the chromatic number (or index) is greater than some specified value k. The parameters of interest, the minimum k- chromatic number and the minimum k-chromatic index consider the least number of failures in the network which could render the network inoperable. In this paper, we consider edge failure, vertex failures, as well as mixed failures for paths, cycles, and complete graphs.