Characterizing properties of permanental polynomials of lollipop graphs
Characterizing properties of permanental polynomials of lollipop graphs
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DOI：
10.1080/03081087.2013.779271
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发表时间：
2014-03
影响因子：
1.1
通讯作者：
Shunyi Liu;Heping Zhang
中科院分区：
文献类型：
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作者：
Shunyi Liu;Heping Zhang
棒棒糖图，用表示，是通过在路径的垂顶点上附加一个循环而得到的图。已知棒棒糖图是由它们的光谱决定的[Haemers WH， Liu X, Zhang Y.]。数学学报，2008;28 (2):1145 - 1145；Boulet R, Jouve b，棒棒糖图由它的光谱决定。电子。[j].生物医学工程学报，2008;15:#R74]。本文考虑了棒棒图是否可以用永久多项式来确定。我们证明（）和（）是由它们的永久多项式决定的，当被限制在连通图上时，通常（）不能由它们的永久多项式决定，即使被限制在连通图上。特别地，我们分别发现了for的不连接的合作伙伴和…和for的连接的合作伙伴。
A lollipop graph, denoted by, is a graph obtained by appending a cycle to a pendant vertex of a path. It is known that the lollipop graphs are determined by their spectra [Haemers WH, Liu X, Zhang Y. Spectral characterizations of lollipop graphs. Linear Algebra Appl. 2008;428:2415–2423; Boulet R, Jouve B. The lollipop graph is determined by its spectrum. Electron. J. Combin. 2008;15:#R74]. In this paper, we consider whether the lollipop graphs can be determined by the permanental polynomial. We show that () and are determined by their permanental polynomials when restricted to connected graphs, and in general () cannot be determined by their permanental polynomials even when restricted to connected graphs. In particular, we find disconnected copermanental mates of for and connected copermanental mates of,,, and for, respectively.