Signed line graphs with least eigenvalue −2: The star complement technique
نویسندگان
چکیده
منابع مشابه
Signed line graphs with least eigenvalue -2: The star complement technique
Let G be a connected graph with least eigenvalue −2, of multiplicity k. A star complement for −2 in G is an induced subgraph H = G − X such that |X | = k and −2 is not an eigenvalue of H . In the case that G is a generalized line graph, a characterization of such subgraphs is used to decribe the eigenspace of −2. In some instances, G itself can be characterized by a star complement. If G is not...
متن کاملGraphs with prescribed star complement for the eigenvalue 1
Let G be a graph of order n and let μ be an eigenvalue of multiplicity m. A star complement for μ in G is an induced subgraph of G of order n−m with no eigenvalue μ. In this paper, we study the maximal graphs as well as regular graphs which have Kr,s + tK1 as a star complement for eigenvalue 1. It turns out that some well known strongly regular graphs are uniquely determined by such a star comp...
متن کاملNotes on graphs with least eigenvalue at least -2
A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. E...
متن کاملPolynomial reconstruction of signed graphs whose least eigenvalue is close to -2
The polynomial reconstruction problem for simple graphs has been considered in the literature for more than forty years and is not yet resolved except for some special classes of graphs. Recently, the same problem has been put forward for signed graphs. Here, the reconstruction of the characteristic polynomial of signed graphs whose vertex-deleted subgraphs have least eigenvalue greater than −2...
متن کاملThe (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 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: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.02.018