Balaji Ramamurthy

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math.CO2021

On resistance matrices of weighted balanced digraphs

R. Balaji, R. B. Bapat, Shivani Goel

Let $G$ be a connected graph with $V (G) = {1, \dots, n}$ . Then the resistance distance between any two vertices $i$ and $j$ is given by $r_{ij} := l_{ii}^{†} + l_{j j}^{†} - 2 l_{ij}^{†}$ , whe…

math.CO2019

Distance matrices perturbed by a Laplacian

Balaji Ramamurthy, Ravindra Bapat, Shivani Goel

Let $T$ be a tree with $n$ vertices. To each edge of $T$ , we assign a weight which is a positive definite matrix of some fixed order, say, $s$ . Let $D_{ij}$ denote the sum of all t…