论文标题
图形的标准化拉普拉斯和相关索引，边缘被集团炸毁
The normalized Laplacian and related indexes of graphs with edges blew up by cliques
论文作者
论文摘要
在本文中，我们介绍了给定图形$ g $的集团Blew Up Graph $ cl（g）$，这是通过用完整的图形$ k_n $替换$ g $的每个边缘来从$ g $获得的。我们表征了给定图$ g $的所有标准化的grpah $ cl（g）$的标准化laplacian光谱。基于获得的频谱，计算乘法度kirchhoff索引的公式，kemeny的常数和$ cl（g）$的跨越树的数量都很好。最后，存在集团布的频谱和索引。
In this paper, we introduce the clique-blew up graph $CL(G)$ of a given graph $G$, which is obtained from $G$ by replacing each edge of $G$ with a complete graph $K_n$. We characterize all the normalized Laplacian spectrum of the grpah $CL(G)$ in term of the given graph $G$. Based on the spectrum obtained, the formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of spanning trees of $CL(G)$ are derived well. Finally, the spectrum and indexes of the clique-blew up iterative graphs are present.
