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Laplacian integral signed graphs with few cycles
AIMS Mathematics 2023, 8(3): 7021-7031
Published: 15 March 2023
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A connected graph with n vertices and m edges is called k-cyclic graph if k = m n + 1. We call a signed graph is Laplacian integral if all eigenvalues of its Laplacian matrix are integers. In this paper, we will study the Laplacian integral k-cyclic signed graphs with k = 0 , 1 , 2 , 3 and determine all connected Laplacian integral signed trees, unicyclic, bicyclic and tricyclic signed graphs.

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