Vol. 11, No. 5, 2018

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The $k$-diameter component edge connectivity parameter

Nathan Shank and Adam Buzzard

Vol. 11 (2018), No. 5, 845–856
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.

Keywords
network reliability, connectivity, conditional connectivity, edge failure, graph theory
Mathematical Subject Classification 2010
Primary: 05C05, 05C12, 05C90, 94C15
Milestones
Received: 11 April 2017
Revised: 22 August 2017
Accepted: 22 August 2017
Published: 2 April 2018

Communicated by Joshua Cooper
Authors
Nathan Shank
Mathematics and Computer Science
Moravian College
Bethlehem, PA
United States
Adam Buzzard
Mathematics and Computer Science
Moravian College
Bethlehem, PA
United States