The k-diameter component edge connectivity parameter

Shank, Nathan; Buzzard, Adam

doi:10.2140/involve.2018.11.845

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The $k$-diameter component edge connectivity parameter

Nathan Shank and Adam Buzzard

Vol. 11 (2018), No. 5, 845–856

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.

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

Vol. 11, No. 5, 2018