The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as   where S is a total dominating set of G and 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.

integrity, domination integrity, total domination integrity, wheel, helm, closed helm, flower graph, generalized web graph

Received: October 28, 2022; Revised: December 17, 2022; Accepted: January 9, 2023; Published: January 25, 2023

How to cite this article: N. H. Shah and P. L. Vihol, Total domination integrity of wheel related graphs, Advances and Applications in Discrete Mathematics 37 (2023), 21-36. http://dx.doi.org/10.17654/0974165823009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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