---
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 >}}