| Summary: | Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></semantics></math></inline-formula> be a simple connected graph with more than one vertex, without loops or multiple edges. A nonempty subset <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi></mrow></semantics></math></inline-formula> is a <i>global offensive alliance</i> if every vertex <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>−</mo><mi>S</mi></mrow></semantics></math></inline-formula> satisfies that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mi>S</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>≥</mo><msub><mi>δ</mi><mover><mi>S</mi><mo>¯</mo></mover></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The <i>global offensive alliance number</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>γ</mi><mi>o</mi></msup><mrow><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is defined as the minimum cardinality among all global offensive alliances. Let <i>R</i> be a finite commutative ring with identity. In this paper, we study the global offensive alliance number of the zero-divisor graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula>.
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