Automorphisms of trivalent graphs

Silvia Benvenuti; Riccardo Piergallini

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arXiv · 1111.3515

Automorphisms of trivalent graphs

Silvia Benvenuti·Riccardo Piergallini

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Abstract

Let $G_{g,b}$ be the set of all uni/trivalent graphs representing the combinatorial structures of pant decompositions of the oriented surface of genus $g$ with $b$ boundary components. We describe the set $A_{g,b}$ of all automorphisms of graphs in $G_{g,b}$ showing that, up to suitable moves changing the graph within $G_{g,b}$, any such automorphism can be reduced to elementary switches of adjacent edges.

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Silvia Benvenuti, Riccardo Piergallini. 2011-11-15. Automorphisms of trivalent graphs. https://arxiv.org/abs/1111.3515

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