ON THE STAR DOMINATION NUMBER IN HYPERGRAPHS

Abstract

The concept of the star domination number  has been previously introduced as a natural extension of domination in graphs and hypergraphs. In this paper, we further investigate its structural properties by establishing general lower and upper bounds for . Additionally, we examine the effect of vertex deletion—both weak and strong—on   for various classes of graphs and hypergraphs, providing characterizations and examples. These results enhance the understanding of the relationship between vertex removal and star domination, offering insights relevant to both theoretical research and practical applications in network resilience.