Characteristics polynomial of normalized Laplacian for trees
نویسندگان
چکیده
منابع مشابه
Characteristics polynomial of normalized Laplacian for trees
Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, Hm(p, q). Moreover, we show that two cospectral Hm(p, q) of the same ...
متن کاملNormalized laplacian spectrum of two new types of join graphs
Let $G$ be a graph without an isolated vertex, the normalized Laplacian matrix $tilde{mathcal{L}}(G)$ is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$, where $mathcal{D}$ is a diagonal matrix whose entries are degree of vertices of $G$. The eigenvalues of $tilde{mathcal{L}}(G)$ are called as the normalized Laplacian eigenva...
متن کاملOn the Coefficients of the Laplacian Characteristic Polynomial of Trees
k=0 (−1)n−k ck(T ) λk . Then, as well known, c0(T ) = 0 and c1(T ) = n . If T differs from the star (Sn) and the path (Pn), which requires n ≥ 5 , then c2(Sn) < c2(T ) < c2(Pn) and c3(Sn) < c3(T ) < c3(Pn) . If n = 4 , then c3(Sn) = c3(Pn) . AMS Mathematics Subject Classification (2000): 05C05, 05C12, 05C50
متن کاملEigenvalues of the normalized Laplacian
A graph can be associated with a matrix in several ways. For instance, by associating the vertices of the graph to the rows/columns and then using 1 to indicate an edge and 0 otherwise we get the adjacency matrix A. The combinatorial Laplacian matrix is defined by L = D − A where D is a diagonal matrix with diagonal entries the degrees and A is again the adjacency matrix. Both of these matrices...
متن کاملLimit points for normalized Laplacian eigenvalues
Limit points for the positive eigenvalues of the normalized Laplacian matrix of a graph are considered. Specifically, it is shown that the set of limit points for the j-th smallest such eigenvalues is equal to [0, 1], while the set of limit points for the j-th largest such eigenvalues is equal to [1, 2]. Limit points for certain functions of the eigenvalues, motivated by considerations for rand...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2015
ISSN: 0096-3003
DOI: 10.1016/j.amc.2015.09.054