DOMINATION INTEGRITY OF SOME NEW GRAPHS
By
N. H. Shah1* and N. J. Kothari2
1Government Polytechnic, Jamnagar, Gujarat, India-361009
2L.E. Colllege Diploma, Morbi, Gujarat, India-363642
Email: nirav.hs@gmail.com (∗Corresponding author), nirang4kothari@gmail.com
(Received: January 16, 2025; In format: February 13, 2025; Revised: April 28, 2025; Accepted: June 06, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55126
Abstract
The domination integrity DI(G) of a simple connected graph G is defined as DI(G) = min{| X | +m(G−X) : X is a dominating set } where m(G−X) is the order of a maximum connected component of G − X. It is a measure of vulnerability of a graph. This work is aimed to discuss domination integrity of middle graph of crown graph, middle graph of tadpole graph, middle graph of friendship graph, christmas Star Graph and kusudama flower graph.
2020 Mathematical Sciences Classification: 05C38, 05C69, 05C76
Keywords and Phrases: Domination Integrity, Integrity, Middle graph, Crown graph