S. Goel

activity

20122021

most citedResistance distance in directed cactus graphs

8 citations · 27 across the 11 of their papers we have counts for

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8 papers · 1 filter

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.CO2021★ 1 cited

Steiner distance matrix of caterpillar graphs

Ali Azimi, R. B. Bapat, Shivani Goel

For a connected graph $G := (V, E)$ , the Steiner distance $d_{G} (X)$ among a set of vertices $X$ is the minimum size among all the connected subgraphs of $G$ whose vertex set contains $…

math.CO2020

On distance matrices of helm graphs obtained from wheel graphs with an even number of vertices

Shivani Goel

Let $n \geq 4$ . The helm graph $H_{n}$ on $2 n - 1$ vertices is obtained from the wheel graph $W_{n}$ by adjoining a pendant edge to each vertex of the outer cycle of $W_{n}$ . Suppose $n$ i…

math.CO2020★ 3 cited

On distance matrices of wheel graphs with odd number of vertices

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

Let $W_{n}$ denote the wheel graph having $n$ -vertices. If $i$ and $j$ are any two vertices of $W_{n}$ , define \[d_{ij}:= \begin{cases} 0 & \mbox{if}~i=j \\ 1 & \mbox{if}~i~ \mbox{and}…

math.CO2020★ 3 cited

An inverse formula for the distance matrix of a wheel graph with even number of vertices

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

Let $n \geq 4$ be an even integer and $W_{n}$ be the wheel graph with $n$ vertices. The distance $d_{ij}$ between any two distinct vertices $i$ and $j$ of $W_{n}$ is the length of the…

math.CO2019★ 8 cited

Resistance distance in directed cactus graphs

Balaji R., Ravindra B. Bapat, Shivani Goel

Let $G = (V, E)$ be a strongly connected and balanced digraph with vertex set $V = {1, \dots, n}$ . The classical distance $d_{ij}$ between any two vertices $i$ and $j$ in $G$ is the mi…

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…

math.CO2019★ 4 cited

Resistance matrices of balanced directed graphs

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

Let $G$ be a strongly connected and balanced directed graph. The Laplacian matrix of $G$ is then the matrix (not necessarily symmetric) $L := D - A$ , where $A$ is the adjacency matrix…