The solvable graph of a finite-dimensional Lie Algebra

Abstract We introduce and investigate the solvable graph $$\Gamma _\mathfrak {S}(L)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Γ</mml:mi> <mml:mi>S</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of a finite-dimensional Lie algebra L over a field F . The vertices are the elements outside the solvabilizer $$\textrm{sol}(L)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/M