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The Graphs Whose Permanental Polynomials Are Symmetric

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Li W.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

233-243

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.

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1 Discussiones Mathematicae Graph Theory

1 Li W.

1 2018

Wyniki wyszukiwania

The Graphs Whose Permanental Polynomials Are Symmetric