【摘要】 研究了路径直积图P_n×P_m的意大利控制数。结合计算机构造证明和数学推导证明，确定了P_n×P₁、P_n×P₂和P_n×P₃的意大利控制数，并给出了P_n×P_m（m≥4）意大利控制数的界。更多还原

【Abstract】 In this paper,the Italian domination number of direct product of paths P_n×P_m is studied. With the combination of computer construction proof and mathematical derivation proof,the exact values of the Italian domination number of P_n×P₁,P_n×P₂ and P_n×P₃ are determined. For P_n×P_m（m≥4）,a bound on the Italian domination number is presented.更多还原