Consider a graph $G=(V, E)$ with $|V|=n$ vertices. Let $(v_1, \dots, v_n)$ be an ordered list of its vertices. Let $G_i=G[\{v_{i+1}, \dots, v_n\}]$ be the induced subgraph on the last $n-i$ vertices. Let $(d_1, \dots, d_n)$ be the degree sequence of $G_i$: $d_i$ is the degree of $v_i$ in $G_i$.
I wonder whether such sequences have been studied, as they raise natural and interesting questions.
For instance, my original motivation is to obtain, for a given graph, such a sequence that is maximum with respect to the majorization order. A natural strategy would be to choose $v_1$ with maximum degree in $G_0$, $v_2$ with maximum degree in $G_1$, and so on. But there is an ambiguity when several vertices have the maximum degree, and other sequences may make sense.
Thank you for any information and suggestions.