Involve: A Journal of Mathematics
- Volume 11, Number 5 (2018), 845-856.
The $k$-diameter component edge connectivity parameter
We focus on a network reliability measure based on edge failures and considering a network operational if there exists a component with diameter or larger. The -diameter component edge connectivity parameter of a graph is the minimum number of edge failures needed so that no component has diameter or larger. This implies each resulting vertex must not have a -neighbor. We give results for specific graph classes including path graphs, complete graphs, complete bipartite graphs, and a surprising result for perfect -ary trees.
Involve, Volume 11, Number 5 (2018), 845-856.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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