𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Laplacian Spectrum of (α, ω) -Graphs

✍ Scribed by Alexander Kelmans

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
111 KB
Volume
23
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

We study the Laplacian spectrum of (α, ω)-graphs which play an important role in the theory of perfect graphs. The properties of the spectrum we found allow the establishment of some structural properties of (α, ω)-graphs. We describe, in particular, a class of graphs that are not subgraphs of (α, ω)-graphs.

📜 SIMILAR VOLUMES

On the conjecture for certain Laplacian
On the conjecture for certain Laplacian integral spectrum of graphs
✍ Kinkar Ch. Das; Sang-Gu Lee; Gi-Sang Cheon 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 184 KB 👁 1 views

## Abstract Let __G__ be a simple graph of order __n__ with Laplacian spectrum {λ~__n__~, λ~__n__−1~, …, λ~1~} where 0=λ~__n__~≤λ~__n__−1~≤⋅≤λ~1~. If there exists a graph whose Laplacian spectrum is __S__={0, 1, …, __n__−1}, then we say that __S__ is Laplacian realizable. In 6, Fallat et al. posed

Pure Point Spectrum for the Laplacian on
Pure Point Spectrum for the Laplacian on Unbounded Nested Fractals
✍ Christophe Sabot 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 208 KB

We prove for the class of nested fractals introduced by T. Lindstro% m (1990, Memoirs Amer. Math. Soc. 420) that the integrated density of states is completely created by the so-called Neuman Dirichlet eigenvalues. The corresponding eigenfunctions lead to eigenfunctions with compact support on the u

On the chromatic spectrum of acyclic dec
On the chromatic spectrum of acyclic decompositions of graphs
✍ Robert E. Jamison; Eric Mendelsohn 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB

## Abstract If __G__ is any graph, a __G‐decomposition__ of a __host__ graph __H__ = (__V__, __E__) is a partition of the edge set of __H__ into subgraphs of __H__ which are isomorphic to __G__. The __chromatic index__ of a __G__‐decomposition is the minimum number of colors required to color the p

On the Spectrum, the Growth, and the Dia
On the Spectrum, the Growth, and the Diameter of a Graph
✍ N. Hajaj 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 171 KB

A lower bound is given for the harmonic mean of the growth in a finite undirected graph 1 in terms of the eigenvalues of the Laplacian of 1. For a connected graph, this bound is tight if and only if the graph is distance-regular. Bounds on the diameter of a ``sphere-regular'' graph follow. Finally,