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+---
+title: "Network Reliability Parameters"
+date: 2023-12-18T00:21:27-05:00
+abstract: >
+    Let $G=(V,E)$ be a finite undirected graph with no isolated vertices.
+    A set $S \subseteq V$ is said to be a total dominating set of $G$ if every vertex in $V$ is adjacent to some vertex in $S$.
+    The total domination number, $\gamma_{t}(G)$, is the minimum cardinality of a total dominating set in $G$.
+    We define the $k$-total bondage to be the minimum number of edges to remove from $G$ so that the resulting graph has a total dominating number at least $k$ more than $\gamma_{t}(G)$.
+    In this work we establish general properties of $k$-total bondage, exact values for certain graph classes including paths, cycles, and wheels, and obtain upper bounds for complete and complete bipartite graphs.
+summary: "$k$-total bondage of Graphs"
+description: "Brief Description of Research"
+math: true
+categories:
+- "Moravian REU 2023"
+tags:
+- "Graph Theory"
+- "Combinatorics"
+---
+
+Peer Researchers
+: Gabriel Fischberg
+: Kyle Kelley
+: Eliel Sosis
+
+Mentors
+: Dr. Nathan Shank
+
+{{< presentations >}}
+## Presentations
+
+* Poster Sessions
+    * [Mathfest 2023](/research/posters/networks_mathfest23.pdf)
+{{< /presentations >}}