Lambda number of the power graph of a finite group
نویسندگان
چکیده
The power graph ΓG of a finite group G is the graph with the vertex set G, where two distinct elements are adjacent if one is a power of the other. An L(2, 1)-labeling of a graph Γ is an assignment of labels from nonnegative integers to all vertices of Γ such that vertices at distance two get different labels and adjacent vertices get labels that are at least 2 apart. The lambda number of Γ, denoted by λ(Γ), is the minimum span over all L(2, 1)-labelings of Γ. In this paper, we obtain bounds for λ(ΓG), and give necessary and sufficient conditions when the bounds are attained. As applications, we compute the exact value of λ(ΓG) if G is a dihedral group, a generalized quaternion group, a P-group or a cyclic group of order pqn, where p and q are distinct primes and n is a positive integer.
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تاریخ انتشار 2017