The permanental polynomial [...] π(G,x)=∑i=0nbixn−i of a graph G is symmetric if bi = bn−i for each i. In this paper, we characterize the graphs with symmetric permanental polynomials. Firstly, we introduce the rooted product H(K) of a graph H by a graph K, and provide a way to compute the permanental polynomial of the rooted product H(K). Then we give a sufficient and necessary condition for the symmetric polynomial, and we prove that the permanental polynomial of a graph G is symmetric if and only if G is the rooted product of a graph by a path of length one.
@article{bwmeta1.element.doi-10_7151_dmgt_1986,
author = {Wei Li},
title = {The Graphs Whose Permanental Polynomials Are Symmetric},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {233-243},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1986}
}
Wei Li. The Graphs Whose Permanental Polynomials Are Symmetric. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 233-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1986/