Abstract
We focus on a network reliability measure based on edge failures and considering a network operational if there exists a component with diameter k or larger. The k-diameter component edge connectivity parameter of a graph is the minimum number of edge failures needed so that no component has diameter k or larger. This implies each resulting vertex must not have a k-neighbor. We give results for specific graph classes including path graphs, complete graphs, complete bipartite graphs, and a surprising result for perfect r-ary trees.
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