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We design succinct encodings of {\it series-parallel, block-cactus} and {\it3-leaf power} graphs while supporting the basic navigational queries such asdegree, adjacency and neighborhood {\it optimally} in the RAM model withlogarithmic word size. One salient feature of our representation is that it canachieve optimal space even though the exact space lower bound for these graphclasses is not known. For these graph classes, we provide succinct datastructures with optimal query support for the first time in the literature. Forseries-parallel multigraphs, our work also extends the works of Uno et al.(Disc. Math. Alg. and Appl., 2013) and Blelloch and Farzan (CPM, 2010) toproduce optimal bounds.

Succinct Data Structures for Series-Parallel, Block-Cactus and 3-Leaf Power Graphs