K. Patra

activity

20102026

most citedVertex connectivity of the power graph of a finite cyclic group

19 citations · 23 across the 20 of their papers we have counts for

collaborators

23 papers

math.OC2026

On Completely Positive and Semidefinite Programs for Moment Bounds on Maximum of Random Quadratics

Buse Unluturk, Divya Padmanabhan, Karthik Natarajan

Completely positive programs are known to provide an exact representation to several NP-hard optimization problems. In this work, we look at the maximum of random quadratic functio…

math.CO2026

Spectral gap of the normalized distance Laplacian

Hitesh Kumar, Kamal Lochan Patra

The smallest positive eigenvalue $\partial_{2}$ of the normalized distance Laplacian matrix $D^{L}$ of a connected graph is called its \emph{spectral gap} and is…

math.CO2026

On the distances between the core center and other central parts of a tree

Akash De, Kamal Lochan Patra

Let $T$ be a tree. For a vertex $v \in V (T)$ , the eccentric subtree number $ε_{T} (v)$ is defined as $ε_{T} (v) = min {f_{T} (v, u) : u \in V (T)}$ where $f_{T} (v, u)$ denotes the number of subtree…

math.GR2025

On the deep commuting graph of a finite group

Sumana Hatui, Sanjay Mukherjee, Kamal Lochan Patra

Let $G$ be a finite group and let $G ~$ be a Schur cover of $G$ . The deep commuting graph $Δ_{D} (G)$ of $G$ is a simple graph with vertex set $G$ , where two distinct vertices a…

math.CO2025

On the minimum cut-sets of the power graph of a finite cyclic group, II

Sanjay Mukherjee, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a finite group $G$ is the simple graph with vertex set $G$ and two distinct vertices are adjacent if one of them is a power of the other. Let $n…

math.GR2022

On the super graphs and reduced super graphs of some finite groups

Sandeep Dalal, Sanjay Mukherjee, Kamal Lochan Patra

For a finite group $G$ , let $B$ be an equivalence (equality, conjugacy or order) relation on $G$ and let $A$ be a (power, enhanced power or commuting) graph with vertex set $G$ . Th…

math.CO2022★ 1 cited

On the minimum cut-sets of the power graph of a finite cyclic group

Sanjay Mukherjee, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a finite group $G$ is the simple graph with vertex set $G$ , in which two distinct vertices are adjacent if one of them is a power of the other.…

math.CO2021

Some new central parts of connected graphs

Dinesh Pandey, Kamal Lochan Patra

The center, median and the security center are three central parts defined for any connected graph whereas the characteristic set, subtree core and core vertices are three central…

math.CO2021

On the minimum degree of power graphs of finite nilpotent groups

Ramesh Prasad Panda, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a group $G$ is the simple graph with vertex set $G$ and two vertices are adjacent whenever one of them is a positive power of the other. In this…

math.GR2021

Characterizing finite nilpotent groups associated with a graph theoretic equality

Ramesh Prasad Panda, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph of a group is the simple graph whose vertices are the group elements and two vertices are adjacent whenever one of them is a positive power of the other. We charact…

math.CO2020

Total eccentricity index of graphs with fixed number of pendant or cut vertices

Dinesh Pandey, Kamal Lochan Patra

The total eccentricity index of a connected graph is defined as sum of the eccentricities of all its vertices. We denote the set of all connected graphs on $n$ vertices with $k$ pe…

math.CO2020

A conjecture on different central parts of binary trees

Dinesh Pandey, Kamal Lochan Patra

Let $Ω_{n}$ be the family of binary trees on $n$ vertices obtained by identifying the root of an rgood binary tree with a vertex of maximum eccentricity of a binary caterpillar. In t…

math.CO2020★ 1 cited

Proper divisor graph of a positive integer

Hitesh Kumar, Kamal Lochan Patra, Binod Kumar Sahoo

The proper divisor graph $Υ_{n}$ of a positive integer $n$ is the simple graph whose vertices are the proper divisors of $n$ , and in which two distinct vertices $u, v$ are adjacent i…

math.CO2019

Wiener index of graphs with fixed number of pendant or cut vertices

Dinesh Pandey, Kamal Lochan Patra

The Wiener index of a connected graph is defined as the sum of the distances between all unordered pair of its vertices. In this paper, we characterize the graphs which extremize t…

math.CO2019

On the minimum degree of the power graph of a finite cyclic group

Ramesh Prasad Panda, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a finite group $G$ is the simple undirected graph whose vertex set is $G$ , in which two distinct vertices are adjacent if one of them is an inte…

math.SP2019

Laplacian eigenvalues of the zero divisor graph of the ring $Z_{n}$

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

We study the Laplacian eigenvalues of the zero divisor graph $Γ (Z_{n})$ of the ring $Z_{n}$ and prove that $Γ (Z_{p^{t}})$ is Laplacia…

math.CO2018★ 2 cited

The core index of a graph

Dinesh Pandey, Kamal Lochan Patra

For a graph $G,$ we denote the number of connected subgraphs of $G$ by $F (G)$ . For a tree $T$ , $F (T)$ has been studied extensively and it has been observed that $F (T)$ has a revers…

math.CO2018

Vertex connectivity of the power graph of a finite cyclic group II

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a given finite group $G$ is the simple undirected graph whose vertices are the elements of $G$ , in which two distinct vertices are adjacent if a…

math.CO2018

Minimal cut-sets in the power graphs of certain finite non-cyclic groups

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph of a group is the simple graph with vertices as the group elements, in which two distinct vertices are adjacent if and only if one of them can be obtained as an int…

math.CO2017★ 19 cited

Vertex connectivity of the power graph of a finite cyclic group

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

Let $n = p_{1}^{n_{1}} p_{2}^{n_{2}} \dots p_{r}^{n_{r}}$ , where $r, n_{1}, \dots, n_{r}$ are positive integers and $p_{1}, p_{2}, \dots, p_{r}$ are distinct prime numbers with $p_{1} < p_{2} < \dots < p_{r}$ . For the…

math.CO2016

Center, centroid and subtree core of trees

Dheer Noal Sunil Desai, Kamal Lochan Patra

For $n \geq 5$ and $2 \leq g \leq n - 3,$ consider the tree $P_{n - g, g}$ on $n$ vertices which is obtained by adding $g$ pendant vertices to one degree $1$ vertex of the path $P_{n - g}$ .…

math.CO2010

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Kamal Lochan Patra, Binod Kumar Sahoo

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ( $n, g$ being fixed), which graph minimizes t…

math.CO2010

Algebraic connectivity of connected graphs with fixed number of pendant vertices

Arbind K. Lal, Kamal L. Patra, Binod K. Sahoo

In this paper we consider the following problem: Over the class of all simple connected graphs of order $n$ with $k$ pendant vertices ( $n, k$ being fixed), which graph maximizes (re…

On Completely Positive and Semidefinite Programs for Moment Bounds on Maximum of Random Quadratics

Spectral gap of the normalized distance Laplacian

On the distances between the core center and other central parts of a tree

On the deep commuting graph of a finite group

On the minimum cut-sets of the power graph of a finite cyclic group, II

On the super graphs and reduced super graphs of some finite groups

On the minimum cut-sets of the power graph of a finite cyclic group

Some new central parts of connected graphs

On the minimum degree of power graphs of finite nilpotent groups

Characterizing finite nilpotent groups associated with a graph theoretic equality

Total eccentricity index of graphs with fixed number of pendant or cut vertices

A conjecture on different central parts of binary trees

Proper divisor graph of a positive integer

Wiener index of graphs with fixed number of pendant or cut vertices

On the minimum degree of the power graph of a finite cyclic group

Laplacian eigenvalues of the zero divisor graph of the ring Zn​

The core index of a graph

Vertex connectivity of the power graph of a finite cyclic group II

Minimal cut-sets in the power graphs of certain finite non-cyclic groups

Vertex connectivity of the power graph of a finite cyclic group

Center, centroid and subtree core of trees

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Algebraic connectivity of connected graphs with fixed number of pendant vertices

Laplacian eigenvalues of the zero divisor graph of the ring $Z_{n}$