1 citations · 1 across the 7 of their papers we have counts for
9 papers
The -Total Bondage Number of a Graph
Jean-Pierre Appel, Gabby Fischberg, Kyle Kelley +2
Let be a connected, finite undirected graph. A set is said to be a total dominating set of if every vertex in is adjacent to some vertex in . T…
On the $nk-attack Roman Dominating Number of a Graph
Garrison Koch, Nathan Shank
Given a graph , the dominating number of a graph is the minimum size of a vertex set, , so that every vertex in the graph is either in or is adjacent…
Graph Coloring as a Measure of Network Vulnerability
Mia Destefano, Grace Mulry, Mason Nakamura +2
We consider new parameters for conditional network vulnerability related to graph coloring. We define a network to be in operation if the chromatic number (or index) is greater tha…
Generalized Bondage Number: The -synchronous bondage number of a graph
Rey Anaya, Alvaro Belmonte, Nathan Shank +2
We investigate a generalization of the bondage number of a graph called the \textit{-synchronous bondage number}. The -synchronous bondage number of a graph is the smalle…
Clumsy Packing of Polyominoes in Finite Space
Emma Miller, Mitchel O'Connor, Nathan Shank
Clumsy packing is considered an inefficient packing, meaning we find the minimum number of objects we can pack into a space so that we can not pack any more object. Thus we are eff…
Vertex and Mixed -Diameter Component Connectivity
Adam Buzzard, Nathan Shank
n the -diameter component connectivity model a network is consider operational if there is a component with diameter at least . Therefore, a network is in a failure state if…
On proportional network connectivity
Ashley Armbruster, Jieqi Di, Nicholas Hanson +1
The reliability of a network is an important parameter to consider when building a network. Different characteristics of the network can become unreliable over time or from other o…
Partisan Combinatorial Game of Edge and Vertex Removal on Graphs
Nathan Shank, Devon Vukovich
We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident…
Extremal Problems Related to the Cardinality Redundance of Graphs
Daniel McGinnis, Nathan Shank
A dominating set of a graph is a set of vertices such that for all , either or for some . The cardinality redundance of a ve…