New York Journal of Mathematics
Volume 25 (2019), 1048-1066


James Stankewicz

On the gonality of graphs and connections to orientable genus

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Published: October 15, 2019.
Keywords: Orientable genus, planar graph, hyperelliptic curve, gonality.
Subject: 05C10, 11G18, 14H51.

We find that hyperelliptic graphs in the sense of Baker and Norine are planar and examine connections between the gonality and orientable genus of a graph. We give a notion of a bielliptic graph and show that each of these must embed into a closed orientable surface of genus one. We also find, for all g ≥ 0, trigonal graphs of orientable genus g, and give analogues for graphs of higher gonality.


Much of this paper was developed in conversation with Spencer Backman. We thank him for numerous ideas. We also thank the anonymous referee for helpful comments.

Author information

James Stankewicz:
Center for Computing Sciences
17100 Science Drive
Bowie, MD 20715, USA