两类交叉四角链的拉普拉斯谱及其应用

Laplacian Spectrum of Two Classes of Linear Crossed Polyomino Chains and its Applications

通过研究线性交叉四角链Xn和交叉四角柱状链Gn的结构特点,利用合成图的拉普拉斯特征值计算出了Xn与Gn的拉普拉斯谱,并且导出了Xn与Gn的基尔霍夫指标,度-基尔霍夫指标和生成树的数目的解析式。且得到当n趋于无穷大时,交叉四角柱状链Gn的基尔霍夫指标是线性交叉四角链Xn的基尔霍夫指标的二分之一。

By studying the structural characteristics of linear crossed polyomino chain Xn and crossed polyomino cylinder chain Gn,the Laplacian spectra of Xn and Gn are calculated by the Laplacian eigenvalues of the composite graph,and the analytic expressions of Kirchhoff index,degree-Kirchhoff index and the number of spanning trees of Xn and Gn are derived.And we show that when n tends to be infinity,the Kirchhoff index of crossed polyomino cylinder chain Gn is one-half of the Kirchhoff index of the linear crossed polyomino chain Xn.