In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.
Otter's Theorem
See also
TreeExplore with Wolfram|Alpha
References
Harary, F. and Prins, G. "The Number of Homeomorphically Irreducible Trees, and Other Species." Acta Math. 101, 141-162, 1959.Otter, R. "The Number of Trees." Ann. Math. 49, 583-599, 1948.Referenced on Wolfram|Alpha
Otter's TheoremCite this as:
Weisstein, Eric W. "Otter's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OttersTheorem.html