Iterated claws have real-rooted genus polynomials

Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker, David G.L. Wang

Research output: Contribution to journalArticlepeer-review


We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertex-amalgamation or iterative edgeamalgamation of graphs that satisfy a commonly observable condition on their partitioned genus distributions, even though it had been proved previously that iterative amalgamation does not always preserve real-rootedness of the genus polynomial of the iterated graph. In this paper, the iterated topological operation is adding a claw, rather than vertex- or edge-amalgamation. Our analysis here illustrates some advantages of employing a matrix representation of the transposition of a set of productions.

Original languageEnglish
Pages (from-to)255-268
Number of pages14
JournalArs Mathematica Contemporanea
Issue number2
StatePublished - 2016


  • Graph genus polynomials
  • Log-concavity
  • Real-rootedness
  • Topological graph theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Iterated claws have real-rooted genus polynomials'. Together they form a unique fingerprint.

Cite this