# The Graphs Whose Permanental Polynomials Are Symmetric

• Volume: 38, Issue: 1, page 233-243
• ISSN: 2083-5892

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## Abstract

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The permanental polynomial [...] π(G,x)=∑i=0nbixn−i $\pi \left(G,x\right)={\sum }_{i=0}^{n}{b}_{i}{x}^{n-i}$ 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.

## How to cite

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Wei Li. "The Graphs Whose Permanental Polynomials Are Symmetric." Discussiones Mathematicae Graph Theory 38.1 (2018): 233-243. <http://eudml.org/doc/288357>.

@article{WeiLi2018,
abstract = {The permanental polynomial [...] π(G,x)=∑i=0nbixn−i $\pi (G,x) = \sum \nolimits _\{i = 0\}^n \{b_i x^\{n - i\} \}$ 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.},
author = {Wei Li},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {permanental polynomial; rooted product; matching},
language = {eng},
number = {1},
pages = {233-243},
title = {The Graphs Whose Permanental Polynomials Are Symmetric},
url = {http://eudml.org/doc/288357},
volume = {38},
year = {2018},
}

TY - JOUR
AU - Wei Li
TI - The Graphs Whose Permanental Polynomials Are Symmetric
JO - Discussiones Mathematicae Graph Theory
PY - 2018
VL - 38
IS - 1
SP - 233
EP - 243
AB - The permanental polynomial [...] π(G,x)=∑i=0nbixn−i $\pi (G,x) = \sum \nolimits _{i = 0}^n {b_i x^{n - i} }$ 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.
LA - eng
KW - permanental polynomial; rooted product; matching
UR - http://eudml.org/doc/288357
ER -

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