S. Goel

activity

20192021

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

3 citations · 7 across the 7 of their papers we have counts for

collaborators

11 papers

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.NT2021

On the distribution of Ramanujan Sums over number fields

Sneha Chaubey, Shivani Goel

For a number field $K$ , and integral ideals $I$ and $J$ in its number ring $O_{K}$ , Nowak studied the asymptotic behaviour of the av…

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.FA2021

Generalized Euclidean distance matrices

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

Euclidean distance matrices (EDM) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized…

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.NT2020

Mean value estimates of gcd and lcm-sums

Sneha Chaubey, Shivani Goel

We study the distribution of the generalized gcd and lcm functions on average. The generalized gcd function, denoted by $(m, n)_{b}$ , is the largest $b$ -th power divisor common to $m$ …