The Graphs Whose Permanental Polynomials Are Symmetric

• Autorzy: Wei Li
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

permanental polynomial; rooted product; matching

Kategorie tematyczne

• 05C31: Graph polynomials
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 38
• Numer: 1
• Strony: 233-243

Daty

wydano

2018-02-01

otrzymano

2016-05-16

zaakceptowano

2016-11-07

online

2017-12-30

Twórcy

autor

Wei Li

• , , Xi’an, , , P.R.

Identyfikatory

DOI

10.7151/dmgt.1986