JournalsaihpdVol. 8, No. 4pp. 537–581

Some results on double triangle descendants of K5K_5

  • Mohamed Laradji

    Burnaby, BC, Canada
  • Marni Mishna

    Simon Fraser University, Burnaby, Canada
  • Karen Yeats

    University of Waterloo, Canada
Some results on double triangle descendants of $K_5$ cover
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Abstract

Double triangle expansion is an operation on 44-regular graphs with at least one triangle which replaces a triangle with two triangles in a particular way. We study the class of graphs which can be obtained by repeated double triangle expansion beginning with the complete graph K5K_5. These are called double triangle descendants of K5K_5. We enumerate, with explicit rational generating functions, those double triangle descendants of K5K_5 with at most four more vertices than triangles. We also prove that the minimum number of triangles in any K5K_5 descendant is four. Double triangle descendants are an important class of graphs because of conjectured properties of their Feynman periods when they are viewed as scalar Feynman diagrams, and also because of conjectured properties of their c2c_2 invariants, an arithmetic graph invariant with quantum field theoretical applications.

Cite this article

Mohamed Laradji, Marni Mishna, Karen Yeats, Some results on double triangle descendants of K5K_5. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), no. 4, pp. 537–581

DOI 10.4171/AIHPD/110