论文标题
归一化的拉普拉斯人和平行细分图的随机步行
The normalized Laplacians and random walks of the parallel subdivision graphs
论文作者
论文摘要
$ k $ - 平行的细分图$ s_k（g）$是由$ g $生成的，每个$ g $的每个边缘都被$ k $的$ k $平行路径替换为长度2。$ 2K $ - 平行的细分图$ s_ {2k {2k}（2k} $均从$ g $ g $ g $ g $ g $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k的parthelly path lenkally path lengther lengther length lenge lenge lenthl path lenthl in s largriptraigh构建。给出了$ s_k（g）$和$ s_ {2k}（g）$的$。他们事实证明，相应的特征值的多重性仅由$ k $确定。作为应用程序，预期的打击时间，预期的通勤时间以及顶点$ i $和$ j $ j $ s_k（g）$之间的任何两点电阻距离，$ s_k（g）$和$ s_k（g）$ s_ {2k}（2k}（g）（g）（g）$的归一化laplacian光谱。此外，分别获得了乘法度kirchhoff索引，凯门尼的常数和$ s_k（g）$，$ s_k^r（g）$，$ s_ {2k}（g）$和$ s_ {2k}^r（g）$的跨度TRESS数量。我们的结果概括了Xie等人的先前作品。和Guo等。分别。
The $k$-parallel subdivision graph $S_k(G)$ is generated from $G$ which each edge of $G$ is replaced by $k$ parallel paths of length 2. The $2k$-parallel subdivision graph $S_{2k}(G)$ is constructed from $G$ which each edge of $G$ is replaced by $k$ parallel paths of length 3. In this paper, the normalized Laplacian spectra of $S_k(G)$ and $S_{2k}(G)$ are given. They turn out that the multiplicities of the corresponding eigenvalues are only determined by $k$. As applications, the expected hitting time, the expected commute time and any two-points resistance distance between vertices $i$ and $j$ of $S_k(G)$, the normalized Laplacian spectra of $S_k(G)$ and $S_{2k}(G)$ with $r$ iterations are given. Moreover, the multiplicative degree Kirchhoff index, Kemeny's constant and the number of spanning tress of $S_k(G)$, $S_k^r(G)$, $S_{2k}(G)$ and $S_{2k}^r(G)$ are respectively obtained. Our results have generalized the previous works in Xie et al. and Guo et al. respectively.
