• Kavitha.M
• Dr.D.G.Akja

The major emphasis of this article is on finitely created groups that embed isometrically into their Cayley graphs, with the goal of demonstrating how these groups may be formed. This allows for the formation of groups that share some of the properties of the graphs in question. Creating a Hilbert space embeddable of groups missing Guoliang Yu's property A, as well as groups whose Cayley graphs certain expanders embed isometrically, is a viable option for many applications. Because these groups are not coarsely embeddable into Hilbert space, the Baum–Connes hypothesis does not hold true for them, and the hypothesis is therefore invalidated. Generally, we depend on small cancellation theory in graphs, and the most challenging technical difficulty is selecting which graphs should have suitable small cancellation labelings. From the discoveries of Fernandez, Leighton, and López-Presa on the uniqueness of r th roots for disconnected graphs in terms of the Cartesian product, it is possible to deduce new cancellation rules.

CANCELLATION PROPERTIES OF PRODUCTS AND SMALL CANCELLATION LABELLINGS OF SOME INFINITE GRAPHS

"CANCELLATION PROPERTIES OF PRODUCTS AND SMALL CANCELLATION LABELLINGS OF SOME INFINITE GRAPHS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 3, page no.d346-d354, March-2022, Available :http://www.jetir.org/papers/JETIR2203347.pdf

"CANCELLATION PROPERTIES OF PRODUCTS AND SMALL CANCELLATION LABELLINGS OF SOME INFINITE GRAPHS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 3, page no. ppd346-d354, March-2022, Available at : http://www.jetir.org/papers/JETIR2203347.pdf