Geodetic Domination Integrity of Thorny Graphs

Abstract

The concept of geodetic domination integrity is a crucial parameter when examining the potential damage to a network. It has been observed that the removal of a geodetic set from the network can increase its vulnerability. This study explores the geodetic domination integrity parameter and presents general results on the geodetic domination integrity values of thorn ring graphs, $n$-sunlet graphs, thorn path graphs, thorn rod graphs, thorn star graphs, helm graphs, $E_p^t$ tree graphs, dendrimer graphs, spider graphs, and bispider graphs, which are the frequently used graph classes in the literature.