There is already a vast amount of literature on degenerate rearrangeme
nts. Graph theory as a tool seems to be used most often with the class
ical chemical approach to understand reaction mechanisms, less often w
ith the analysis of NMR spectra as influenced by rearrangement process
es, and seldom with the analysis of rovibronic spectra and the role of
permutation-inversion group. Here we show how the graph-theoretical a
pproach can be used to study the rovibronic spectral problem. The grap
h-theoretical procedure to estimate the zero-order splitting for rotat
ional and vibrational quantum numbers J=K=M=O and upsilon = 0, 1 is el
aborated in detail for the internal rotation of ethane and for the Ber
ry-pseudorotation of the trigonal bipyramidal skeleton (as for PFS).