W. Barrett

activity

20062023

most citedSparsity of Graphs that Allow Two Distinct Eigenvalues

1 citations · 3 across the 9 of their papers we have counts for

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Showing 2017 · math.COShow all

3 papers · 2 filters

math.CO2017

Resistance distance in straight linear 2-trees

Wayne Barrett, Emily J. Evans, Amanda E. Francis

We consider the graph $G_{n}$ with vertex set $V (G_{n}) = {1, 2, \dots, n}$ and ${i, j} \in E (G_{n})$ if and only if $0 < ∣ i - j ∣ \leq 2$ . We call $G_{n}$ the straight linear 2-tree on $n…

math.CO2017

Resistance distance in bent linear 2-trees

Wayne Barrett, Emily J. Evans, Amanda E. Francis

In this note we consider the bent linear 2-tree and provide an explicit formula for the resistance distance $r_{G_{n}} (1, n)$ between the first and last vertices of the graph. We call…

math.CO2017

The inverse eigenvalue problem of a graph: Multiplicities and minors

Wayne Barrett, Steve Butler, Shaun M. Fallat +5

The inverse eigenvalue problem of a given graph $G$ is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in $G…