منابع مشابه
Spectra of signed adjacency matrices
A signed adjacency matrix is a {−1, 0, 1}-matrix A obtained from the adjacency matrix A of a simple graph G by symmetrically replacing some of the 1’s of A by −1’s. Bilu and Linial have conjectured that if G is k-regular, then some A has spectral radius ρ(A) ≤ 2 √ k − 1. If their conjecture were true then, for each fixed k > 2, it would immediately guarantee the existence of infinite families o...
متن کاملBipartite theory of Semigraphs
Given a semigraph, we can construct graphs Sa, Sca, Se and S1e. In the same pattern, we construct bipartite graphs CA(S), A(S), VE(S), CA(S) and A(S). We find the equality of domination parameters in the bipartite graphs constructed with the domination and total domination parameters of the graphs Sa and Sca. We introduce the domination and independence parameters for the bipartite semigraph. W...
متن کاملHyper Domination in Bipartite Semigraphs
Let S be a bipartite semigraph with |NXa(y)| ≥ 1 for every y ∈ Y . A vertex x ∈ X hyper dominates y ∈ Y if y ∈ Na(x) or y ∈ Na(NY a(x)). A subsetD ⊆ X is a hyper dominating set of S if every y ∈ Y is hyper dominated by a vertex ofD. A subsetD ⊆ X is called a minimal hyper dominating set of S if no proper subset of D is a hyper dominating set of S. The minimum cardinality of a minimal hyper domi...
متن کاملSome Applications of the Proper and Adjacency Polynomials in the Theory of Graph Spectra
Given a vertex u ∈ V of a graph Γ = (V,E), the (local) proper polynomials constitute a sequence of orthogonal polynomials, constructed from the so-called u-local spectrum of Γ. These polynomials can be thought of as a generalization, for all graphs, of the distance polynomials for the distance-regular graphs. The (local) adjacency polynomials, which are basically sums of proper polynomials, wer...
متن کاملLower Bound on the Chromatic Number by Spectra of Weighted Adjacency Matrices
A lower bound on the chromatic number of a graph is derived by majorization of spectra of weighted adjacency matrices. These matrices are given by Hadamard products of the adjacency matrix and arbitrary Hermitian matrices.
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 Mathematics, Algorithms and Applications
سال: 2023
ISSN: ['1793-8309', '1793-8317']
DOI: https://doi.org/10.1142/s1793830923500118