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Graph Coloring as a Measure of Network Vulnerability

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arxiv 2212.01284 v1 pith:OHMQQUZC submitted 2022-12-02 math.CO

Graph Coloring as a Measure of Network Vulnerability

Mia Destefano , Grace Mulry , Mason Nakamura , Rodrigo Rios , Nathan Shank This is my paper
classification math.CO
keywords networkconsiderfailuresnumberchromaticcoloringgraphindex
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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.

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