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2018 The $k$-diameter component edge connectivity parameter
Nathan Shank, Adam Buzzard
Involve 11(5): 845-856 (2018). DOI: 10.2140/involve.2018.11.845

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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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

Information

Received: 11 April 2017; Revised: 22 August 2017; Accepted: 22 August 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 1385.05043
MathSciNet: MR3784030
Digital Object Identifier: 10.2140/involve.2018.11.845

Subjects:
Primary: 05C05, 05C12, 05C90, 94C15

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2018
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