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A simple graph is reflexive if the second largest eigenvalue of its (0, 1)- adjacency matrix does not exceed 2. A vertex of the cycle of unicyclic simple graph is said to be loaded if its degree is greater than 2. In this paper we establish that the length of the cycle of unicyclic reflexive graph with seven loaded vertices is at most 10 and find all such graphs with the length of the cycle 10, 9 and 8.

Unicyclic reflexive graphs with seven loaded vertices of the cycle