Abstract
Edges that are the unique chords of at least one cycle have been studied by a variety of authors over the past dozen years. This paper begins the study of those graphs in which each edge is the unique chord of exactly one cycle. The [Formula: see text]-connected planar graphs that enjoy this restriction are characterized by two infinite sequences (the dipyramid and trapezohedron [Formula: see text]-polytopes) together with three special graphs (the [Formula: see text]-antiprism, and the [Formula: see text]- and [Formula: see text]-prism graphs).
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