R. Merris, The Laplacian permanental polynomial for trees,
Czech. Math. J. 32 (1982), 397-403. Math Reviews 84a:05047.
The main result of this article is a combinatorial interpretation
for the coefficients in the Laplacian permanental polynomial,
per(xI-L(T)), of a tree T. It follows,
for any connected graph G on n vertices, that per(L(G)) > 2(n-1),
with equality if and only if G is the star. This affirmatively resolves
a conjecture in article
49. Among the publications citing this paper
are:
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