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A signed graph is an ordered pair <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>=</mo><mo>(</mo><mi>G</mi><mo>,</mo><mi>σ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, where <i>G</i> is a graph and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo lspace="0pt">:</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⟶</mo><mo>{</mo><mo>+</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula> is a mapping. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>(</mo><mi>e</mi><mo>)</mo></mrow></semantics></math></inline-formula> is called the sign of <i>e</i> and for any sub-graph <i>H</i> of <i>G</i>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow><mo>=</mo><mstyle displaystyle="true"><munder><mo>∏</mo><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></munder></mstyle><mi>σ</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is called the sign of <i>H</i>. A signed graph having a sign of each cycle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> is called balanced. Two vertices in a graph <i>G</i> are called antipodal if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi>G</mi></msub><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>m</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. The antipodal graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> of a graph <i>G</i> is the graph with a vertex set that is the same as that of <i>G</i>, and two vertices <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> are adjacent if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></semantics></math></inline-formula> are antipodal. By the <i>d</i>-antipodal graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>G</mi><mi>d</mi><mi>A</mi></msubsup></semantics></math></inline-formula> of a graph <i>G</i>, we refer to the union of <i>G</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula>. Given a signed graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>=</mo><mo>(</mo><mi>G</mi><mo>,</mo><mi>σ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, the signed graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mo>Σ</mo><mrow><mi>d</mi></mrow><mi>A</mi></msubsup><mo>=</mo><mrow><mo>(</mo><msubsup><mi>G</mi><mi>d</mi><mi>A</mi></msubsup><mo>,</mo><msub><mi>σ</mi><mi>d</mi></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is called the <i>d</i>-antipodal signed graph of <i>G</i>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>σ</mi><mi>d</mi></msub></semantics></math></inline-formula> is defined as follows: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>d</mi></msub><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow><mo>=</mo><mi>σ</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow><mspace width="4.pt"></mspace><mi>if</mi><mspace width="4.pt"></mspace><mi>e</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mspace width="4.pt"></mspace><mi>and</mi><mspace width="4.pt"></mspace><mrow><mi>otherwise</mi><mo>,</mo></mrow><mspace width="4.pt"></mspace><msub><mi>σ</mi><mi>d</mi></msub><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow><mo>=</mo><mstyle displaystyle="true"><munder><mo>∏</mo><mrow><mi>P</mi><mo>∈</mo><msub><mi mathvariant="script">P</mi><mi>e</mi></msub></mrow></munder></mstyle><mi>σ</mi><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">P</mi><mi>e</mi></msub></semantics></math></inline-formula> is the collection of all diametric paths in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Σ</mo></semantics></math></inline-formula> connecting the end vertices of an antipodal edge <i>e</i> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mo>Σ</mo><mi>d</mi><mi>A</mi></msubsup></semantics></math></inline-formula>. In this article, the balance property and canonical consistency of <i>d</i>-antipodal signed graphs of Smith signed graphs (connected graphs having a highest eigenvalue of 2) are studied.