# A note on sub-total domination in graphs

## TL;DR

This paper introduces the sub-total domination number, a new graph invariant based on degree sequences, which provides a lower bound for the well-known total domination number in graphs without isolated vertices.

## Contribution

The paper defines the sub-total domination number and establishes its role as a lower bound for the total domination number in simple graphs.

## Key findings

- Sub-total domination number is a new degree sequence derived invariant.
- It serves as a lower bound for the total domination number.
- The concept applies to graphs without isolated vertices.

## Abstract

Let $G$ be a simple and finite graph without isolated vertices. In this paper we introduce and study a new degree sequence derived invariant called the \emph{sub-total domination number}, denoted $\sub_t(G)$. In particular, we show that $\sub_t(G)$ serves as a lower bound on $\gamma_t(G)$, where $\gamma_t(G)$ denotes the heavily studied \emph{total domination number} of $G$.