Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 5 (2018), 845-856.

The $k$-diameter component edge connectivity parameter

Nathan Shank and Adam Buzzard

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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.

Article information

Source
Involve, Volume 11, Number 5 (2018), 845-856.

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1523498547

Digital Object Identifier
doi:10.2140/involve.2018.11.845

Mathematical Reviews number (MathSciNet)
MR3784030

Zentralblatt MATH identifier
1385.05043

Subjects
Primary: 05C05: Trees 05C12: Distance in graphs 05C90: Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 94C15: Applications of graph theory [See also 05Cxx, 68R10]

Keywords
network reliability connectivity conditional connectivity edge failure graph theory

Citation

Shank, Nathan; Buzzard, Adam. The $k$-diameter component edge connectivity parameter. Involve 11 (2018), no. 5, 845--856. doi:10.2140/involve.2018.11.845. https://projecteuclid.org/euclid.involve/1523498547


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References

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