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A realizer of a triangulated plane graph G is a partition of interior edges of G, satisfying some conditions. The realizer has many applications, including graph drawing algorithms. Given a triangulated plane graph G, no algorithm to generate all realizers of G is known. In this paper, we first give an algorithm to generate all realizers. We first define a left canonical ordering for the vertices of an input graph, then show that there is a bijection between the left canonical orderings and realizers. Based on the bijection, we give an algorithm to generate all realizers. The algorithm generates each realizer in O(n) time without duplications, where n is the number of vertices in the graph. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 89(7): 40–47, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20276 [ABSTRACT FROM AUTHOR]