English

Graph Coloring as a Measure of Network Vulnerability

Combinatorics 2022-12-05 v1

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.

Keywords

Cite

@article{arxiv.2212.01284,
  title  = {Graph Coloring as a Measure of Network Vulnerability},
  author = {Mia Destefano and Grace Mulry and Mason Nakamura and Rodrigo Rios and Nathan Shank},
  journal= {arXiv preprint arXiv:2212.01284},
  year   = {2022}
}

Comments

13 pages, 1 picture

R2 v1 2026-06-28T07:20:38.487Z