This thesis introduces a new graph-theoretic structure —the (2, \ (-connected sequence —with direct applicability to the embedding of both planar and nonplanar graphs. It is proven that: (1) the nodes of a graph can be ordered so as to form a (2, \ (-connected sequence, regardless of whether the graph is planar or nonplanar, and (2) such a sequence yields a new and exceptionally simple technique for planarity testing and embedding. All algorithms are proven to operate within a time bound proportional to the square of the number of nodes or edges in the graph. Accepted for the Air Force Joseph R. Waterman, I.t. Col., USAF Chief, Lincoln Laboratory Project Office "Thesis submitted to the Division of Engineering and Applied Physics at Harvard University in June 197 1 in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Applied Mathematics.