"centered on the notion of" is a correct and usable phrase in written English.
You could use it to express the idea that something is focused on a certain idea or concept. For example: "This book is centered on the notion of family dynamics and how they can affect our psychological health."
These charges and issues are centered on the notion of his otherness, that he's not a "real American".
Instead, Searle's discussions of linguistic meaning have often centered on the notion of intentionality.
The theory of rationality supposedly generated by Laudan's methodology is centered on the notion of the research tradition.
This theory is centered on the notion of what he calls 'suggestion', or the evincing in us by our sensory data of concepts corresponding to the qualities of things in the world.
It's best to paraphrase, but essentially the opposing comment centered on the notion of sex, and how people don't want to know about, or even disapprove of, what gay people do in the bedroom.
Here, the concepts of life course development and family formation are much less centered on the notion of stability and economic certainty, but instead the concept of balance and of the mutual reciprocity of two life spheres is emphasized.
There are a number of objections to Searle's account including the following ones centering on the notion of collective acceptance in play and its relation to deontic properties and associated powers.
It centers on the notion of black men as "perpetual suspects" -- in other words, racial profiling, a subject much in the news right now.
Other cost models are centered on the notion that the act of generating an erroneous product can be costly in itself ("process cost").
Discussion centered on the notion that we appear to be breeding ourselves out of existence and what to do about it.
Given the delicate political nature of the documents released by WikiLeaks, chatter in technology circles immediately centered on the notion that a government body had spearheaded the disruptions.
