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Pritam Majumder
Pritam Majumder
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What information does the automorphism group $\mathrm{Aut}(G)$ of a graph $G$ give us about the number of it's spanning trees?

If not in general, can anything be said about some special cases, for example, when $\mathrm{Aut}(G)$ is the symmetric group $S_r$ for some $r\leq |V(G)|$? What if $G$ is regular/strongly regular?

What information does the automorphism group $\mathrm{Aut}(G)$ of a graph $G$ give us about the number of it's spanning trees?

If not in general, can anything be said about some special cases, for example, when $\mathrm{Aut}(G)$ is the symmetric group $S_r$ for some $r\leq |V(G)|$?

What information does the automorphism group $\mathrm{Aut}(G)$ of a graph $G$ give us about the number of it's spanning trees?

If not in general, can anything be said about some special cases, for example, when $\mathrm{Aut}(G)$ is the symmetric group $S_r$ for some $r\leq |V(G)|$? What if $G$ is regular/strongly regular?

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Pritam Majumder
Pritam Majumder
  • 1.3k
  • 11
  • 22

Number of spanning trees from the automorphism group

What information does the automorphism group $\mathrm{Aut}(G)$ of a graph $G$ give us about the number of it's spanning trees?

If not in general, can anything be said about some special cases, for example, when $\mathrm{Aut}(G)$ is the symmetric group $S_r$ for some $r\leq |V(G)|$?