Abstract
We focus on a network reliability measure based on edge failures and considering a network operational if there exists a component with diameter or larger. The -diameter component edge connectivity parameter of a graph is the minimum number of edge failures needed so that no component has diameter or larger. This implies each resulting vertex must not have a -neighbor. We give results for specific graph classes including path graphs, complete graphs, complete bipartite graphs, and a surprising result for perfect -ary trees.
Citation
Nathan Shank. Adam Buzzard. "The $k$-diameter component edge connectivity parameter." Involve 11 (5) 845 - 856, 2018. https://doi.org/10.2140/involve.2018.11.845
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