The power graph \(\Gamma _G\) of a finite group G is the graph with the vertex set G, where two distinct elements are adjacent if and only if one is a power of the other. An L(2, 1)-labeling of a graph \(\Gamma \) is an assignment of labels from nonnegative integers to all vertices of \(\Gamma \) such that vertices at distance two get different labels and adjacent vertices get labels that are at least 2 apart. The lambda number of \(\Gamma \), denoted by \(\lambda (\Gamma )\), is the minimum span or range over all L(2, 1)-labelings of \(\Gamma \). In this paper, we obtain bounds for \(\lambda (\Gamma _G)\) and give necessary and sufficient conditions when the bounds are attained. As applications, we compute the exact value of \(\lambda (\Gamma _G)\) if G is a dihedral group, a generalized quaternion group, a \({\mathcal {P}}\)-group or a cyclic group of order \(pq^n\), where p and q are distinct primes and n is a positive integer.

有限群G的幂图\（\ Gamma _G \）是顶点集G的图，其中两个不同的元素在且仅当一个是另一个的幂时才相邻。图\（\ Gamma \）的L（2，1）-标签是从非负整数到\（\ Gamma \）所有顶点的标签分配，这样距离2的顶点获得不同的标签，相邻顶点获得标签至少相隔2 \（\ Gamma \）的lambda数，用\（\ lambda（\ Gamma）\）表示，是\（\ Gamma \）的所有L（2，1）标签上的最小跨度或范围。在本文中，我们获得\（\ lambda（\ Gamma _G）\）的边界，并给出达到边界的必要和充分条件。作为应用程序，如果G是二面体组，广义四元数组，\（{\ mathcal {P}} \）-组或循环组，我们将计算\（\ lambda（\ Gamma _G）\）的精确值阶\（pq ^ n \），其中p和q是不同的质数，n是正整数。