On the inverse signed total domination number in graphs

TL;DR

This paper investigates the inverse signed total domination number in graphs, establishing new bounds and characterizations, including a sharp upper bound for graphs without large complete subgraphs and for trees based on their structure.

Contribution

It introduces new bounds and characterizations for the inverse signed total domination number, applying classical theorems and structural analysis of trees.

Findings

Sharp upper bound for graphs with no large induced complete subgraph

Bounds for trees based on order and number of leaves

Characterization of trees attaining the bounds

Abstract

In this paper, we study the inverse signed total domination number in graphs and present new lower and upper bounds on this parameter. For example by making use of the classic theorem of Turan (1941), we present a sharp upper bound for graphs with no induced complete subgraph of order greater than two. Also, we bound this parameter for a tree in terms of its order and the number of leaves and characterize all trees attaining this bound.