New bounds on the signed total domination number of graphs

TL;DR

This paper establishes new sharp bounds on the signed total domination number of graphs, including specific bounds for graphs excluding complete subgraphs and for trees with support vertices, along with characterizations of extremal trees.

Contribution

The paper introduces novel sharp bounds for the signed total domination number, utilizing Turan's theorem and characterizing extremal trees achieving these bounds.

Findings

Sharp lower bound for graphs with no K_{r+1} subgraph.

Upper bound for trees based on support vertices.

Characterization of trees attaining the upper bound.

Abstract

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turan, we present a sharp lower bound on this parameter for graphs with no complete graph of order r+1 as a subgraph. Also, we prove that n-2(s-s') is an upper bound on the signed total domination number of any tree of order n with s support vertices and s' support vertives of degree two. Moreover, we characterize all trees attainig this bound.