THE (NORMALIZED) LAPLACIAN EIGENVALUE OF SIGNED GRAPHS
نویسندگان
چکیده
منابع مشابه
The (normalized) Laplacian Eigenvalue of Signed Graphs
Abstract. A signed graph Γ = (G, σ) consists of an unsigned graph G = (V, E) and a mapping σ : E → {+,−}. Let Γ be a connected signed graph and L(Γ),L(Γ) be its Laplacian matrix and normalized Laplacian matrix, respectively. Suppose μ1 ≥ · · · ≥ μn−1 ≥ μn ≥ 0 and λ1 ≥ · · · ≥ λn−1 ≥ λn ≥ 0 are the Laplacian eigenvalues and the normalized Laplacian eigenvalues of Γ, respectively. In this paper, ...
متن کاملNote on the normalized Laplacian eigenvalues of signed graphs
The normalized Laplacian of a graph was introduced by F.R.K. Chung and has been studied extensively over the last decade. In this paper, we introduce the notion of the normalized Laplacian of signed graphs and extend some fundamental concepts of the normalized Laplacian from graphs to signed graphs.
متن کاملOn net-Laplacian Energy of Signed Graphs
A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the ei...
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 Spectrum of the Normalized Laplacian for Signed Graphs: Interlacing, Contraction, and Replication
We consider the normalized Laplacian matrix for signed graphs and derive interlacing results for its spectrum. In particular, we investigate the effects of several basic graph operations, such as edge removal and addition and vertex contraction, on the Laplacian eigenvalues. We also study vertex replication, whereby a vertex in the graph is duplicated together with its neighboring relations. Th...
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: Taiwanese Journal of Mathematics
سال: 2015
ISSN: 1027-5487
DOI: 10.11650/tjm.19.2015.4675