## One Citation

### Paths are generically realisable

- Mathematics
- 2021

We show that every 0-1 multiplicity matrix for a simple graph G is generically realisable for G. In particular, every multiplicity matrix for a path is generically realisable. We use this result to…

## References

SHOWING 1-10 OF 22 REFERENCES

### Smith Normal Form and acyclic matrices

- Mathematics
- 2005

An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter…

### Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph

- MathematicsElectron. J. Comb.
- 2017

Two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities, and are referred to as the Strong Spectral Property and the Strong Multiplicity Property.

### Minimum number of distinct eigenvalues of graphs

- Mathematics
- 2013

The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven…

### ON THE MINIMUM NUMBER OF DISTINCT EIGENVALUES FOR A SYMMETRIC MATRIX WHOSE GRAPH IS A GIVEN TREE

- Mathematics
- 2002

It is shown that for any tree T the minimum number of distinct eigenvalues of an Hermitian matrix whose graph is T (diagonal entries free) is at least the number of vertices in a longest path of T.…

### A lower bound for the number of distinct eigenvalues of some real symmetric matrices

- Mathematics
- 2010

This mostly expository note surveys and recovers a lower bound for the number of distinct eigenvalues of real symmetric matrices associated with a graph. The relation is established with the length…

### Achievable multiplicity partitions in the inverse eigenvalue problem of a graph

- MathematicsSpecial Matrices
- 2019

Abstract Associated to a graph G is a set 𝒮(G) of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and…

### Combinatorial Matrix Classes

- Mathematics
- 1991

1. Introduction 2. Basic existence theorems for matrices with prescribed properties 3. The class A(R S) of (0,1)-matrices 4. More on the class A(R S) of (0,1)-matrices 5. The class T(R) of tournament…

### Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph

- Mathematics
- 2017

We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply these to determine…