cycle | graph chord

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C. For example, in the diamond graph as labeled above, the edge (3, 4) is a chord of the cycle (1, 3, 2, 4, 1). The motivation for the term "chord" is geometric. In particular, if a cycle is drawn with its vertices lying on the a circle and its chords are drawn as line segments, then the chords of the cycle are chords of the circle. Graph bridges are not chords since they do not lie on a cycle. Similarly, in order to lie on a cycle, both endpoints of a chord must be of vertex degree at least 3.

chord | chordal graph | chordless cycle | chordless graph | graph cycle | Meyniel graph