R. K. Nath

activity

20102026

most citedFinite groups whose commuting graphs are integral

12 citations · 42 across the 47 of their papers we have counts for

collaborators

54 papers

math.RA2026

Minimum second neighborhood degree energy of commuting graphs of finite rings

Payal Tak, Jutirekha Dutta, Rajat Kanti Nath

In this paper, we compute minimum second neighborhood degree spectrum and energy of commuting graphs of certain finite non-commutative rings. In particular, we consider non-commuta…

math.CO2026

Certain topological indices and spectral properties of SGB-graphs of finite cyclic groups

Shrabani Das, Ahmad Erfanian, Rajat Kanti Nath

Let $L (G)$ be the set of all subgroups of a group $G$ . The subgroup generating bipartite graph $B (G)$ defined on $G$ is a bipartite graph whose vertex set is the union of…

math.GR2026

Various spectra and energies of subgroup generating bipartite graph

Shrabani Das, Ahmad Erfanian, Rajat Kanti Nath

Let $L (G)$ be the set of all subgroups of a group $G$ . The subgroup generating bipartite graph $B (G)$ defined on $G$ is a bipartite graph whose vertex set is partitioned…

math.CO2025

Various spectral aspects of NCCC-graphs of certain finite non-abelian groups

Rishabh Chakraborty, Firdous Ee Jannat, Rajat Kanti Nath

Let $G$ be a finite non-abelian group. The non-commuting conjugacy class graph (abbreviated as NCCC-graph) of $G$ is a simple undirected graph whose vertex set is the set of conj…

math.GR2025

Zagreb indices of subgroup generating bipartite graph

Shrabani Das, Ahmad Erfanian, Rajat Kanti Nath

Let $G$ be a group and $L (G)$ be the set of all subgroups of $G$ . The subgroup generating bipartite graph $B (G)$ defined on $G$ is a bipartite graph whose vertex set is p…

math.GR2024

On a bipartite graph defined on groups

Shrabani Das, Ahmad Erfanian, Rajat Kanti Nath

Let $G$ be a group and $L (G)$ be the set of all subgroups of $G$ . We introduce a bipartite graph $B (G)$ on $G$ whose vertex set is the union of two sets $G \times G$ and…

math.GR2024

Commuting Conjugacy Class Graphs of Finite Groups and the Hansen-Vukičević Conjecture

Shrabani Das, Rajat Kanti Nath, Yilun Shang

In this work, we compute the first and second Zagreb indices for the commuting conjugacy class graphs associated with finite groups. We identify multiple classes of finite groups w…

math.GR2024

Engel and co-Engel graphs of finite groups

Peter J. Cameron, Rishabh Chakraborty, Rajat Kanti Nath +1

Let $G$ be a group. Associate a directed graph $E (G)$ (called the Engel digraph of $G$ ) with $G$ whose vertex set is $G$ , with an arc $(x, y)$ if $[y,_{k} x] = 1$ for some posi…

math.CO2024

Main functions and the spectrum of super graphs

G. Arunkumar, Peter J. Cameron, R. Ganeshbabu +1

Let A be a graph type and B an equivalence relation on a group $G$ . Let $[g]$ be the equivalence class of $g$ with respect to the equivalence relation B. The B superA graph of $G$ …

math.GR2024★ 1 cited

Super commuting graphs of finite groups and their Zagreb indices

Shrabani Das, Rajat Kanti Nath

Let $B$ be an equivalence relation defined on a finite group $G$ . The $B$ super commuting graph on $G$ is a graph whose vertex set is $G$ and two distinct vertices $g$ and $h$ are…

math.GR2024

A survey on conjugacy class graphs of groups

P. J. Cameron, F. E. Jannat, R. K. Nath +1

There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group $G$ and adjacency is defined by properties of the e…

math.GR2024

Common neighborhood (signless) Laplacian spectrum and energy of CCC-graph

Firdous Ee Jannat, Rajat Kanti Nath

In this paper, we consider commuting conjugacy class graph (abbreviated as CCC-graph) of a finite group $G$ which is a graph with vertex set ${x^{G} : x \in G ∖ Z (G)}$ (whe…

math.GR2024

Common neighborhood Laplacian and signless Laplacian spectra and energies of commuting graphs

Firdous Ee Jannat, Rajat Kanti Nath

In this paper, we compute common neighbourhood Laplacian spectrum, common neighbourhood signless Laplacian spectrum and their respective energies of commuting graph of some finite…

math.CO2024

Common neighborhood energies and their relations with Zagreb index

Firdous Ee Jannat, Rajat Kanti Nath, Kinkar Chandra Das

In this paper we establish connections between common neighborhood Laplacian and common neighborhood signless Laplacian energies and the first Zagreb index of a graph $G$ …

math.GR2024

Super graphs on groups, II

G. Arunkumar, Peter J. Cameron, Rajat Kanti Nath

In an earlier paper, the authors considered three types of graphs, and three equivalence relations, defined on a group, viz.\ the power graph, enhanced power graph, and commuting g…

math.GR2024

Characterization of commuting graphs of finite groups having small genus

Shrabani Das, Deiborlang Nongsiang, Rajat Kanti Nath

In this paper we first show that among all double-toroidal and triple-toroidal finite graphs only $K_{8} ⊔ 9 K_{1}$ , $K_{8} ⊔ 5 K_{2}$ , $K_{8} ⊔ 3 K_{4}$ , $K_{8} ⊔ 9 K_{3}$ , $K_8\s…

math.GR2023★ 1 cited

Zagreb indices of commuting and non-commuting graphs of finite groups and Hansen-Vukičević conjecture

Shrabani Das, Arpita Sarkhel, Rajat Kanti Nath

In this paper we compute first and second Zagreb indices of commuting and non-commuting graphs of finite groups and determine several classes of finite groups such that their commu…

math.GR2023★ 1 cited

Signless Laplacian energies of non-commuting graphs of finite groups and related results

Monalisha Sharma, Rajat Kanti Nath

The non-commuting graph of a non-abelian group $G$ with center $Z (G)$ is a simple undirected graph whose vertex set is $G ∖ Z (G)$ and two vertices $x, y$ are adjacent if $xy…

math.GR2022

Common neighbourhood spectrum and energy of commuting conjugacy class graph

Firdous Ee Jannat, Rajat Kanti Nath

In this paper we compute common neighbourhood (abbreviated as CN) spectrum and energy of commuting conjugacy class graph of several families of finite non-abelian groups. As a cons…

math.CO2021

Super graphs on groups, I

G. Arunkumar, Peter J. Cameron, Rajat Kanti Nath +1

Let $G$ be a finite group. A number of graphs with the vertex set $G$ have been studied, including the power graph, enhanced power graph, and commuting graph. These graphs form a h…

math.CO2021

Geometry of logarithmic derivations of hyperplane arrangements

Avi Steiner, Graham Denham

We study the Hadamard product of the linear forms defining a hyperplane arrangement with those of its dual, which we view as generating an ideal in a certain polynomial ring. We us…

math.RA2021

Genus of commuting graphs of some classes of finite rings

Walaa Nabil Taha Fasfous, Rajat Kanti Nath

In this paper, we compute the genus of commuting graphs of non-commutative rings of order $p^{4}$ , $p^{5}$ , $p^{2} q$ and $p^{3} q$ , where $p$ and $q$ are prime integers. We also characteriz…

math.GR2020

$g$ -noncommuting graph of a finite group relative to its subgroups

Monalisha Sharma, Rajat Kanti Nath

Let $H$ be a subgroup of a finite non-abelian group $G$ and $g \in G$ . Let $Z (H, G) = {x \in H : x y = y x, \forall y \in G}$ . We introduce the graph $Δ_{H, G}^{g}$ whose vertex set…

math.GR2020

Relative g-noncommuting graph of finite groups

Monalisha Sharma, Rajat Kanti Nath

Let $G$ be a finite group. For a fixed element $g$ in $G$ and a given subgroup $H$ of $G$ , the relative $g$ -noncommuting graph of $G$ is a simple undirected graph whose vertex set…

Minimum second neighborhood degree energy of commuting graphs of finite rings

Certain topological indices and spectral properties of SGB-graphs of finite cyclic groups

Various spectra and energies of subgroup generating bipartite graph

Various spectral aspects of NCCC-graphs of certain finite non-abelian groups

Zagreb indices of subgroup generating bipartite graph

On a bipartite graph defined on groups

Commuting Conjugacy Class Graphs of Finite Groups and the Hansen-Vukičević Conjecture

Engel and co-Engel graphs of finite groups

Main functions and the spectrum of super graphs

Super commuting graphs of finite groups and their Zagreb indices

A survey on conjugacy class graphs of groups

Common neighborhood (signless) Laplacian spectrum and energy of CCC-graph

Common neighborhood Laplacian and signless Laplacian spectra and energies of commuting graphs

Common neighborhood energies and their relations with Zagreb index

Super graphs on groups, II

Characterization of commuting graphs of finite groups having small genus

Zagreb indices of commuting and non-commuting graphs of finite groups and Hansen-Vukičević conjecture

Signless Laplacian energies of non-commuting graphs of finite groups and related results

Common neighbourhood spectrum and energy of commuting conjugacy class graph

Super graphs on groups, I

Geometry of logarithmic derivations of hyperplane arrangements

Genus of commuting graphs of some classes of finite rings

g-noncommuting graph of a finite group relative to its subgroups

Relative g-noncommuting graph of finite groups

$g$ -noncommuting graph of a finite group relative to its subgroups