On the Largest Eigenvalue of a Random Subgraph of the Hypercube

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Abstract

Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely \lambda_1= ) max,np), where \Delta is the maximum degree of G and o term tends to zero as max, np) tends to infinity.

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