Abstract
A multi-fan graph is a graph of the form ( P n 1 + P n 2 + ⋯ + P n k ) × b , where b is a universal vertex, and P n 1 + P n 2 + ⋯ + P n k is the disjoint union of paths P n i ( n i ⩾ 1 ) for i = 1 , 2 , … , k . In particular, if k = 1 , the multi-fan graph P n 1 × b is the classical fan graph F n 1 + 1 . It is proved that all the multi-fan graphs are determined by their Laplacian spectra.
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