### May 10, 2021

**Amélia Durbec**(LIS, Aix Marseille University)

Consider a network that evolves reversibly, according to

nearest neighbours interactions. Can its dynamics create/destroy nodes?

On the one hand, since the nodes are the principal carriers of information,

it seems that they cannot be destroyed without jeopardising bijectivity.

On the other hand, there are plenty of global functions from graphs to

graphs that are non-vertex-preserving and bijective. The question has

been answered negatively—in three different ways. Yet, in this paper we

do obtain reversible local node creation/destruction—in three relaxed

settings, whose equivalence we prove for robustness. We motivate our

work both by theoretical computer science considerations (reversible

computing, cellular automata extensions) and theoretical physics concerns

(basic formalisms towards discrete quantum gravity).