# The Graphs Whose Permanental Polynomials Are Symmetric

Discussiones Mathematicae Graph Theory (2018)

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

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topWei 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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