  Coupled Map Lattice (CML) models are particularly suitable to study spatially
extended behaviours, such as wave-like patterns, spatio-temporal chaos, and
synchronisation. Complete synchronisation in CMLs emerges when all maps have
their state variables with equal magnitude, forming a spatially-uniform pattern
that evolves in time. Here, we derive critical values for the parameters --
coupling strength, maximum Lyapunov exponent, and link density -- that control
the synchronisation-manifold's linear stability of diffusively-coupled,
identical, chaotic maps in generic regular graphs (i.e., graphs with uniform
node degrees) and class-specific cyclic graphs (i.e., periodic lattices with
cyclical node permutation symmetries). Our derivations are based on the
Laplacian matrix eigenvalues, where we give closed-form expressions for the
smallest non-zero eigenvalue and largest eigenvalue of regular graphs and show
that these graphs can be classified into two sets according to a topological
condition (derived from the stability analysis). We also make derivations for
two classes of cyclic graph: $k$-cycles (i.e., regular lattices of even degree
$k$, which can be embedded in $T^k$ tori) and $k$-M\"obius ladders, which we
introduce here to generalise the M\"obius ladder of degree $k = 3$. Our results
highlight differences in the synchronisation manifold's stability of these
graphs -- even for identical node degrees -- in the finite size and infinite
size limit.
