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TOTAL DOMINATION INTEGRITY OF WHEEL RELATED GRAPHS
Keywords:
integrity, domination integrity, total domination integrity, wheel, helm, closed helm, flower graph, generalized web graphDOI:
https://doi.org/10.17654/0974165823009Abstract
The total domination integrity of a simple connected graph $G$ with no isolated vertices is denoted by $T D I(G)$ and defined as $T D I(G)=\min \{|S|+m(G-S): S \subseteq V(G)\}$, where $S$ is a total dominating set of $G$ and $m(G-S)$ is the order of a maximum connected component of $G-S$. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.
Received: October 28, 2022;
Revised: December 17, 2022;
Accepted: January 9, 2023;
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