A. Francis

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20172024

most citedAlgorithmic techniques for finding resistance distances on structured graphs

1 citations · 1 across the 2 of their papers we have counts for

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math.CO2021★ 1 cited

Algorithmic techniques for finding resistance distances on structured graphs

E. J. Evans, A. E. Francis

In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent…

math.CO2019

Spanning 2-Forests and Resistance Distance in 2-Connected Graphs

Wayne Barrett, Emily J. Evans, Amanda E. Francis +2

A spanning 2-forest separating vertices $u$ and $v$ of an undirected connected graph is a spanning forest with 2 components such that $u$ and $v$ are in distinct components. Aside…

math.CO2018

General Equitable Decompositions for Graphs with Symmetries

Amanda Francis, Dallas Smith, Benjamin Webb

Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices wh…

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…