S. Goel

activity

20122021

most citedResistance distance in directed cactus graphs

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

collaborators

12 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 $m$ …

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…

cs.OH2012★ 8 cited

Vulnerability Management for an Enterprise Resource Planning System

Shivani Goel, Ravi Kiran, Deepak Garg

Enterprise resource planning (ERP) systems are commonly used in technical educational institutions(TEIs). ERP systems should continue providing services to its users irrespective o…