# On a Class of Graphs with Large Total Domination Number

## TL;DR

This paper characterizes a broad family of graphs, including chordal graphs, where the total domination number equals twice the domination number, extending previous results and addressing an open question in graph theory.

## Contribution

It provides a characterization of graphs satisfying b3_t(G) = 2b3(G), generalizing earlier work and partially answering an open problem.

## Key findings

- Characterization of graphs with b3_t(G) = 2b3(G)
- Includes chordal graphs as a special case
- Extends previous theoretical results

## Abstract

Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total domination number, respectively, of a graph $G$ with no isolated vertices. It is well-known that $\gamma_t(G) \leq 2\gamma(G)$. We provide a characterization of a large family of graphs (including chordal graphs) satisfying $\gamma_t(G)= 2\gamma(G)$, strictly generalizing the results of Henning (2001) and Hou et al. (2010), and partially answering an open question of Henning (2009).