  We study the problem of checking the existence of a step-by-step
transformation of $d$-regular induced subgraphs in a graph, where $d \ge 0$ and
each step in the transformation must follow a fixed reconfiguration rule. Our
problem for $d=0$ is equivalent to \textsc{Independent Set Reconfiguration},
which is one of the most well-studied reconfiguration problems. In this paper,
we systematically investigate the complexity of the problem, in particular, on
chordal graphs and bipartite graphs. Our results give interesting contrasts to
known ones for \textsc{Independent Set Reconfiguration}.
