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In 1994, Dobrynin and Kochetova introduced the concept of <i>degree distance</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">DD</mo><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></semantics></math></inline-formula> of a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mo>Γ</mo></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> be the Steiner <i>k</i>-distance of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></semantics></math></inline-formula>. The <i>Steiner Wiener k-index</i> or <i>k-center Steiner Wiener index</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula> is defined by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow><mo>=</mo><msub><mo>∑</mo><mover><mrow><mo>|</mo><mi>S</mi><mo>|</mo><mo>=</mo><mi>k</mi></mrow><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mover></msub><msub><mi>d</mi><mo>Γ</mo></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mo>.</mo></mrow></semantics></math></inline-formula> The <i>k-center Steiner degree distance</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula> is defined by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow><mo>=</mo><msub><mo>∑</mo><mover><mrow><mo>|</mo><mi>S</mi><mo>|</mo><mo>=</mo><mi>k</mi></mrow><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mover></msub><mfenced separators="" open="[" close="]"><msub><mo>∑</mo><mrow><mi>v</mi><mo>∈</mo><mi>S</mi></mrow></msub><mi>d</mi><mi>e</mi><msub><mi>g</mi><mo>Γ</mo></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mfenced><msub><mi>d</mi><mo>Γ</mo></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>e</mi><msub><mi>g</mi><mo>Γ</mo></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is the degree of the vertex <i>v</i> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>. In this paper, we consider the Nordhaus–Gaddum-type results for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Upper bounds on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow><mo>+</mo><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mover><mo>Γ</mo><mo>¯</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow><mo>·</mo><msub><mo form="prefix">SW</mo><mi>k</mi></msub><mrow><mo>(</mo><mover><mo>Γ</mo><mo>¯</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are obtained for a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula> and compared with previous bounds. We present sharp upper and lower bounds of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow><mo>+</mo><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mover><mo>Γ</mo><mo>¯</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow><mo>·</mo><msub><mo form="prefix">SDD</mo><mi>k</mi></msub><mrow><mo>(</mo><mover><mo>Γ</mo><mo>¯</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> for a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula> of order <i>n</i> with maximum degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula> and minimum degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>. Some graph classes attaining these bounds are also given.