Interlacing eigenvalues on some operations of graphs
نویسندگان
چکیده
منابع مشابه
Interlacing Eigenvalues and Graphs
We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a maximal (colclique, the chromatic number, the diameter, and the bandwidth, in terms of the eigenvalues of the Standard adjacency matrix or the Laplacian matrix. We also deal with inequalities and regularity resu...
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
متن کاملOn the eigenvalues of non-commuting graphs
The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.
متن کاملSome Applications of Laplace Eigenvalues of Graphs Some Applications of Laplace Eigenvalues of Graphs
In the last decade important relations between Laplace eigenvalues and eigenvectors of graphs and several other graph parameters were discovered. In these notes we present some of these results and discuss their consequences. Attention is given to the partition and the isoperimetric properties of graphs, the max-cut problem and its relation to semideenite programming, rapid mixing of Markov cha...
متن کاملInterlacing adjoints on directed graphs
For an integer k ≥ 1, the k-th interlacing adjoint of a digraph G is the digraph ιk(G) with vertex-set V (G) k , and arcs ((u1, . . . , uk), (v1, . . . , vk)) such that (ui, vi) ∈ A(G) for i = 1, . . . , k and (vi, ui+1) ∈ A(G) for i = 1, . . . , k − 1. For every k we derive upper and lower bounds for the chromatic number of ιk(G) in terms of that of G. In particular, we find tight bounds on 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: Linear Algebra and its Applications
سال: 2009
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.10.018