  We design succinct encodings of {\it series-parallel, block-cactus} and {\it
3-leaf power} graphs while supporting the basic navigational queries such as
degree, adjacency and neighborhood {\it optimally} in the RAM model with
logarithmic word size. One salient feature of our representation is that it can
achieve optimal space even though the exact space lower bound for these graph
classes is not known. For these graph classes, we provide succinct data
structures with optimal query support for the first time in the literature. For
series-parallel multigraphs, our work also extends the works of Uno et al.
(Disc. Math. Alg. and Appl., 2013) and Blelloch and Farzan (CPM, 2010) to
produce optimal bounds.
