Double triangle expansion is an operation on -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 . These are called double triangle descendants of . We enumerate, with explicit rational generating functions, those double triangle descendants of with at most four more vertices than triangles. We also prove that the minimum number of triangles in any 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 invariants, an arithmetic graph invariant with quantum field theoretical applications.
Publié le :
DOI : 10.4171/aihpd/110
Mots-clés : Double triangle reduction/expansion, $K_5$-descendants, zigzags, $n$-zigzags, $\phi^4$ theory, constant $c_2$-invariant.
@article{AIHPD_2021__8_4_537_0, author = {Laradji, Mohamed and Mishna, Marni and Yeats, Karen}, title = {Some results on double triangle descendants of $K_5$}, journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D}, pages = {537--581}, volume = {8}, number = {4}, year = {2021}, doi = {10.4171/aihpd/110}, mrnumber = {4337448}, zbl = {1479.05156}, language = {en}, url = {http://archive.numdam.org/articles/10.4171/aihpd/110/} }
TY - JOUR AU - Laradji, Mohamed AU - Mishna, Marni AU - Yeats, Karen TI - Some results on double triangle descendants of $K_5$ JO - Annales de l’Institut Henri Poincaré D PY - 2021 SP - 537 EP - 581 VL - 8 IS - 4 UR - http://archive.numdam.org/articles/10.4171/aihpd/110/ DO - 10.4171/aihpd/110 LA - en ID - AIHPD_2021__8_4_537_0 ER -
%0 Journal Article %A Laradji, Mohamed %A Mishna, Marni %A Yeats, Karen %T Some results on double triangle descendants of $K_5$ %J Annales de l’Institut Henri Poincaré D %D 2021 %P 537-581 %V 8 %N 4 %U http://archive.numdam.org/articles/10.4171/aihpd/110/ %R 10.4171/aihpd/110 %G en %F AIHPD_2021__8_4_537_0
Laradji, Mohamed; Mishna, Marni; Yeats, Karen. Some results on double triangle descendants of $K_5$. Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 4, pp. 537-581. doi : 10.4171/aihpd/110. http://archive.numdam.org/articles/10.4171/aihpd/110/
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