Abstract
A graph G is called a 1-planar graph if G has a drawing in the plane, so that each of its edges is crossed at most once. In this paper, we prove that λ1(G)≤5+2n+5 for a 1-planar graph G of order n≥7. For n≥6.23×1018, we characterize the unique extremal graph with the maximum spectral radius among all 1-planar graphs of order n.
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