✦ LIBER ✦

Trees with very few eigenvalues

✍ Scribed by Robert A. Beezer

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 381 KB
Volume: 14
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190140415

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The number of distinct eigenvalues of the adjacency matrix of a graph is bounded below by the diameter of the graph plus one. Many graphs that achieve this lower bound exhibit much symmetry, for example, distance‐transitive and distance‐regular graphs. Here we provide a recursive construction that will create graphs having the fewest possible eigenvalues. This construction is best at creating trees, but will also create cyclic graphs meeting the lower bound. Unlike the graphs mentioned above, many of the graphs constructed do not exhibit large amounts of symmetry. A corollary allows us to determine the values and multiplicities of all the nonsimple eigenvalues of the constructed graph.

📜 SIMILAR VOLUMES

Intersection representation of digraphs

Intersection representation of digraphs in trees with few leaves

✍ Lin, In-Jen; Sen, Malay K.; West, Douglas B. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 285 KB 👁 2 views

The leafage of a digraph is the minimum number of leaves in a host tree in which it has a subtree intersection representation. We discuss bounds on the leafage in terms of other parameters (including Ferrers dimension), obtaining a string of sharp inequalities.

On the embedding of graphs into graphs w

On the embedding of graphs into graphs with few eigenvalues

✍ Vu, Van H. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 726 KB

A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic

Computation of a Few Small Eigenvalues o

Computation of a Few Small Eigenvalues of a Large Matrix with Application to Liquid Crystal Modeling

✍ J. Baglama; D. Calvetti; L. Reichel; A. Ruttan 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 374 KB

Equilibrium configurations of liquid crystals in a finite containment are minimizers of the thermodynamic free energy of the system. It is important to be able to track an equilibrium configuration as the temperature of the liquid crystals is decreased. The path of the minimal energy configuration a

EIGENVALUES OF RADIALLY SYMMETRIC MODES

EIGENVALUES OF RADIALLY SYMMETRIC MODES IN COMPOSITE SPHERICAL DOMAINS WITH A VERY SMALL CONCENTRIC CAVITY

✍ C.A. ROSSIT; P.A.A. LAURA 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 79 KB

Certainly, when dealing with an unsteady thermoelastic situation, the presence of a cavity of small radius will generate severe stress concentration.

Immunological focusing by the mouse majo

Immunological focusing by the mouse major histocompatibility complex: Mouse strains confronted with distantly related lysozymes confine their attention to very few epitopes

✍ Michael E. Katz; Richard M. Maizels; Linda Wicker; Alexander Miller; Eli E. Serc 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 622 KB

Iterative methods for the calculation of

Iterative methods for the calculation of a few of the lowest eigenvalues and corresponding eigenvectors of the AX = λBX equation with real symmetric matrices of large dimension

✍ Alexander V. Mitin 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 326 KB

New methods for the iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of a generalized eigenvalue problem are proposed. These methods use only multiplication of the A and B matrices on a vector. 0 1994 by John Wiley & Sons, Inc.