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

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.

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

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