arXiv subjects

Jitender Kumar

Publications and source records attributed to Jitender Kumar.

At least 19 recordsLinked to original sources

arXiv2026

On the vertex connectivity of weakly zero-divisor graph of commutative rings

The weakly zero-divisor graph $W\Gamma(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$, and two distinct vertices $x$, $y$ are adjacent if and only if there $w\in {\rm ann}(x)$ and $ z\in {\rm ann}(y)$ such that $wz =0$. In this paper, we obtain the vertex connectivity of $W\Gamma(R)$, where $R$ is an Artinian ring or reduced ring. Indeed, for these rings, we prove that the vertex connectivity of $W\Gamma(R)$ is equal to its minimum degree. This paper also characterizes all the vertices of minimum degree of $W\Gamma(R)$.

math.AC↗

arXiv2026

On embeddings of the difference graph of the intersection power graph and the power graph

The power graph of a finite group $G$ is a simple undirected graph with vertex set $G$ and two vertices are adjacent if one is a power of the other. The intersection power graph of a finite group $G$ is a simple undirected graph with vertex set $G$ and two vertices $x$, $y$ are adjacent if $\langle x\rangle \cap \langle y \rangle \neq \{e\}$. The difference graph $\mathcal{D}(G)$ of a finite group $G$ is the difference of the intersection power graph $\mathcal{G}_{1}(G)$ and power graph $\mathcal{P}(G)$ with all isolated vertices removed. We characterized all the finite nilpotent groups $G$ such that the difference graph is planar. Further, we determine all the finite nilpotent groups whose difference graph has genus at most $2$. Moreover, we prove that there does not exist any group whose difference graph is projective planar.

math.GR↗

arXiv2026

Probing GHz Spin Dynamics Across Magnetic Phase Transitions in CrCl3 Nanoflakes Using Nitrogen-Vacancy Microscopy

CrCl3, a layered van der Waals (vdW) magnet, exhibits in-plane magnetic anisotropy and enhanced interlayer coupling upon stacking, making it an ideal platform to host exotic nanoscale magnetic phenomena such as magnon hydrodynamics and meron-like topological spin defects. When interfaced with other vdW materials, its antiferromagnetic-to-ferromagnetic and ferromagnetic-to-paramagnetic phase transitions and magnetic anisotropy can be tuned by voltage, strain, and layer stacking. Understanding the spin dynamics of CrCl3 at its magnetic phase transitions is crucial to its applications in magnonics. Here, we investigate the spin dynamics of CrCl3 nanoflakes using cryogenic diamond quantum sensing microscopy, based on measuring optically detected magnetic resonance, Rabi oscillations, and spin-lattice relaxation time (T1) of shallow nitrogen vacancy (NV) centers in diamond. In the ferromagnetic regime, we observe a pronounced reduction in the NV spin resonance contrast, a collapse of the Rabi oscillations, and a strong enhancement by two orders of magnitude of the relaxation rate G1 = 1/T1. These observations indicate intensified spin fluctuations in the gigahertz range. Broadband ferromagnetic resonance spectroscopy on CrCl3 crystals reveals resonance frequencies in the 4-15 GHz range together with a linewidth of ~24 mT, further supporting the NV measurements. A phenomenological model of magnetic-noise-induced NV relaxation reproduces the temperature dependence of G1 by combining antiferromagnetic, ferromagnetic, and paramagnetic fluctuation channels, indicating that magnetic noise is strongest in the ferromagnetic regime and evolves markedly across the phase transition. These results are crucial for using CrCl3 in 2D magnonics and hybrid quantum-magnon systems.

cond-mat.mes-hall↗

arXiv2026

Metric Dimension of Difference Graph of Finite Groups

The Difference graph $\mathcal{D}(G)$ of a finite group $G$ is the difference of the enhanced power graph $\mathcal{P}_{E}(G)$ and the power graph $\mathcal{P}(G)$ with all the isolated vertices removed. In this paper, we characterize the vertex set of the difference graph of finite nilpotent groups and obtain its cardinality. Consequently, we obtain the metric dimension of the difference graph of finite nilpotent groups. Moreover, this paper determines the metric dimension of the difference graphs of certain non-nilpotent groups, namely: dihedral groups, the generalized quaternion groups, and the semi-dihedral groups.

math.GR↗

arXiv2025

Spin Dynamics in the van der Waals Ferromagnet CrTe2 Engineered by Niobium Doping

Understanding and controlling spin dynamics in two-dimensional (2D) van der Waals (vdW) ferromagnets is essential for their application in magnonics and hybrid quantum platforms. Here, we investigate the spin dynamics of the vdW ferromagnet 1T-CrTe_{2} and demonstrate their systematic tunability via niobium (Nb) substitution in Cr_{1-x}Nb_{x}Te_{2}(x=0-0.2). Ferromagnetic resonance (FMR) spectroscopy reveals that Nb doping enables wide-band tuning of the resonance frequency from 40 GHz down to the few-GHz regime, accompanied by a moderate increase in the Gilbert damping constant from ~0.066 to ~0.14, while preserving robust room-temperature ferromagnetism. Complementary magnetometry shows a concurrent reduction of the Curie temperature and saturation magnetization with increasing Nb content. Density functional theory calculations attribute the observed spin-dynamic trends to Nb-induced modifications of magnetic anisotropy and magnetic exchange interactions. Furthermore, CrTe_{2} flakes (~80 nm thick) exhibit lower resonance frequencies and damping than bulk crystals, consistent with thickness, surface/interface, and shape-dependent magnetic anisotropy. These results establish Nb-doped CrTe_{2} as a tunable vdW ferromagnet with controllable spin dynamics, extending its functionality from spintronics to broadband magnonics and quantum magnonics.

cond-mat.mtrl-sci↗

arXiv2025

A Cytology Dataset for Early Detection of Oral Squamous Cell Carcinoma

Oral squamous cell carcinoma OSCC is a major global health burden, particularly in several regions across Asia, Africa, and South America, where it accounts for a significant proportion of cancer cases. Early detection dramatically improves outcomes, with stage I cancers achieving up to 90 percent survival. However, traditional diagnosis based on histopathology has limited accessibility in low-resource settings because it is invasive, resource-intensive, and reliant on expert pathologists. On the other hand, oral cytology of brush biopsy offers a minimally invasive and lower cost alternative, provided that the remaining challenges, inter observer variability and unavailability of expert pathologists can be addressed using artificial intelligence. Development and validation of robust AI solutions requires access to large, labeled, and multi-source datasets to train high capacity models that generalize across domain shifts. We introduce the first large and multicenter oral cytology dataset, comprising annotated slides stained with Papanicolaou(PAP) and May-Grunwald-Giemsa(MGG) protocols, collected from ten tertiary medical centers in India. The dataset is labeled and annotated by expert pathologists for cellular anomaly classification and detection, is designed to advance AI driven diagnostic methods. By filling the gap in publicly available oral cytology datasets, this resource aims to enhance automated detection, reduce diagnostic errors, and improve early OSCC diagnosis in resource-constrained settings, ultimately contributing to reduced mortality and better patient outcomes worldwide.

eess.IV↗

arXiv2025

Sensing single molecule magnets with nitrogen vacancy centers

Single-molecule magnets (SMMs) are molecules that can function as nanoscale magnets with potential use as magnetic memory bits. While SMMs can retain magnetization at low temperatures, characterizing them on surface and at room temperature remains challenging and requires specialized nanoscale techniques. Here, we use single nitrogen-vacancy (NV) centers in diamond as highly sensitive, broadband magnetic field sensors to detect the magnetic noise of cobalt-based SMMs deposited on a diamond surface. We measure the NV relaxation and decoherence times at 296 K and at 5-8 K, observing a significant influence of the SMMs on them. From this, we can infer the SMMs' magnetic noise spectral density (NSD) and underlying magnetic properties. Moreover, we observe the effect of an applied magnetic field on the SMMs' NSD at low temperatures. The method provides nanoscale sensitivity for characterizing SMMs under realistic conditions relevant to their use as surface-bound memory units.

quant-ph↗

arXiv2025

Sombor index and eigenvalues of weakly zero-divisor graph of commutative rings

The weakly zero-divisor graph $W\Gamma(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two distinct vertices $x$, $y$ are adjacent if and only if there exist $w\in {\rm ann}(x)$ and $ z\in {\rm ann}(y)$ such that $wz =0$. In this paper, we determine the Sombor index for the weakly zero-divisor graph of the integers modulo ring $\mathbb{Z}_n$. Furthermore, we investigate the Sombor spectrum and establish bounds for the Sombor energy of the weakly zero-divisor graph of $\mathbb{Z}_n$.

math.CO↗

arXiv2025

Sombor Spectrum of Super Graphs defined on groups

Given a simple graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super $A$ graph is defined as a simple graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if either they are in the same equivalence class or there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that $g^{\prime}$ and $h^{\prime}$ are adjacent in $A$. In the literature, the $B$ super $A$ graphs have been investigated by considering $A$ to be either power graph, enhanced power graph, or commuting graph and $B$ to be an equality, order or conjugacy relation. In this paper, we investigate the Sombor spectrums of these $B$ super $A$ graphs for certain non-abelian groups, viz. the dihedral group, generalized quaternion group and the semidihedral group, respectively.

math.CO↗

arXiv2024

Laplacian Spectrum of Super Graphs defined on Certain Non-abelian Groups

Given a graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super$A$ graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if and only if there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that $g^{\prime}$ and $h^{\prime}$ are adjacent in $A$. Recently, Dalal \emph{et al.} (Spectrum of super commuting graphs of some finite groups, \textit{Computational and Applied Mathematics}, 43(6):348, 2024) obtain the Laplacian spectrum of supercommuting graphs of certain non-abelian groups including the dihedral group and the generalized quaternion group. In this paper, we continue the study of Laplacian spectrum of certian $B$ super$A$ graphs. We obtain the Laplacian spectrum of conjugacy superenhanced power graphs of certain non-abelian groups, namely: dihedral group, generalized quaternion group and semidihedral group. Moreover to enhance the work of Dalal \emph{et al}, we obtain the Laplacian spectrum of conjugacy supercommuting graph of semidihedral group. We prove that graphs considered in this paper are $L$-integral.

math.CO↗

arXiv2024

The embedding of line graphs associated to the annihilator graph of commutative rings

The annihilator graph $AG(R)$ of the commutative ring $R$ is an undirected graph with vertex set as the set of all non-zero zero divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $ann(xy) \neq ann(x) \cup ann(y)$. In this paper, we study the embedding of the line graph of $AG(R)$ into orientable or non-orientable surfaces. We completely characterize all the finite commutative rings such that the line graph of $AG(R)$ is of genus or crosscap at most two. We also obtain the inner vertex number of $L(AG(R))$. Finally, we classify all the finite rings such that the book thickness of $L(AG(R))$ is at most four.

math.CO↗

arXiv2024

On the minimal (edge) connectivity of graphs and its applications to power graphs of finite groups

In an earlier work, finite groups whose power graphs are minimally edge connected have been classified. In this article, first we obtain a necessary and sufficient condition for an arbitrary graph to be minimally edge connected. Consequently, we characterize finite groups whose enhanced power graphs and order superpower graphs, respectively, are minimally edge connected. Moreover, for a finite non-cyclic group $G$, we prove that $G$ is an elementary abelian $2$-group if and only if its enhanced power graph is minimally connected. Also, we show that $G$ is a finite $p$-group if and only if its order superpower graph is minimally connected. Finally, we characterize all the finite nilpotent groups such that the minimum degree and the vertex connectivity of their order superpower graphs are equal.

math.GR↗

arXiv2024

On line upper ideal relation graphs of rings

The upper ideal relation graph $\Gamma_{U}(R)$ of a commutative ring $R$ with unity is a simple undirected graph with the set of all non-unit elements of $R$ as a vertex set and two vertices $x$, $y$ are adjacent if and only if the principal ideals $(x)$ and $(y)$ are contained in the principal ideal $(z)$ for some non-unit element $z\in R$. This manuscript characterizes all the Artinian rings $R$ such that the graph $\Gamma_{U}(R)$ is a line graph. Moreover, all the Artinian rings $R$ for which $\Gamma_{U}(R)$ is the complement of a line graph have been described.

math.CO↗

arXiv2024

Strong Resolving Graphs of Clean Graphs of Commutative Rings

Let $R$ be a ring with unity. The clean graph $\text{Cl}(R)$ of a ring $R$ is the simple undirected graph whose vertices are of the form $(e,u)$, where $e$ is an idempotent element and $u$ is a unit of the ring $R$ and two vertices $(e,u)$, $(f,v)$ of $\text{Cl}(R)$ are adjacent if and only if $ef = fe =0$ or $uv = vu=1$. In this manuscript, for a commutative ring $R$, first we obtain the strong resolving graph of $\text{Cl}(R)$ and its independence number. Using them, we determine the strong metric dimension of the clean graph of an arbitrary commutative ring. As an application, we compute the strong metric dimension of $\text{Cl}(R)$, where $R$ is a commutative Artinian ring.

math.CO↗

arXiv2024

Genus and crosscap of Normal subgroup based power graphs of finite groups

Let $H$ be a normal subgroup of a group $G$. The normal subgroup based power graph $\Gamma_H(G)$ of $G$ is the simple undirected graph with vertex set $V(\Gamma_H(G))= (G\setminus H)\cup \{e\}$ and two distinct vertices $a$ and $b$ are adjacent if either $aH = b^m H$ or $bH=a^nH$ for some $m,n \in \mathbb{N}$. In this paper, we continue the study of normal subgroup based power graph and characterize all the pairs $(G,H)$, where $H$ is a non-trivial normal subgroup of $G$, such that the genus of $\Gamma_H(G)$ is at most $2$. Moreover, we determine all the subgroups $H$ and the quotient groups $\frac{G}{H}$ such that the cross-cap of $\Gamma_H(G)$ is at most three.

math.CO↗

arXiv2024

Upper ideal relation graphs associated to rings

Let $R$ be a ring with unity. The upper ideal relation graph $\Gamma_U(R)$ of the ring $R$ is a simple undirected graph whose vertex set is the set of all non-unit elements of $R$ and two distinct vertices $x, y$ are adjacent if and only if there exists a non-unit element $z \in R$ such that the ideals $(x)$ and $(y)$ contained in the ideal $(z)$. In this article, we classify all the non-local finite commutative rings whose upper ideal relation graphs are split graphs, threshold graphs and cographs, respectively. In order to study topological properties of $\Gamma_U(R)$, we determine all the non-local finite commutative rings $R$ whose upper ideal relation graph has genus at most $2$. Further, we precisely characterize all the non-local finite commutative rings for which the crosscap of $\Gamma_U(R)$ is either $1$ or $2$.

math.RA↗

arXiv2023

Room temperature relaxometry of single nitrogen-vacancy centers in proximity to $\alpha$-RuCl$_3$ nanoflakes

Investigating spin and charge noise in strongly correlated electron systems is a valuable way to analyze their physical properties and unlock new phases of matter. In this context, nitrogen-vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use longitudinal relaxation time $T_1$ of single NV centers to investigate the spin dynamics of nanometers-thin flakes of $\alpha$-RuCl$_3$ at room temperature. We observe a significant reduction in the $T_1$ in the presence of $\alpha$-RuCl$_3$ in proximity to our NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal plane. Furthermore, the $T_1$ time exhibits an almost linear increase with an applied external magnetic field. We associate this trend with the alteration of spin and charge noise in $\alpha$-RuCl$_3$ under an external magnetic field. These findings suggest that the influence of the room-temperature spin dynamics of $\alpha$-RuCl$_3$ on the longitudinal relaxation time of the NV center can be used to gain information on the material itself and the technique to be used on other 2D materials.

cond-mat.mes-hall↗

arXiv2023

Line graph characterization of the order supergraph of a finite group

The power graph $\mathcal{P}(G)$ is the simple undirected graph with group elements as a vertex set and two elements are adjacent if one of them is a power of the other. The order supergraph $\mathcal{S}(G)$ of the power graph $\mathcal{P}(G)$ is the simple undirected graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if $o(x)\vert o(y)$ or $o(y)\vert o(x)$. In this paper, we classify all the finite groups $G$ such that the order supergraph $\mathcal{S}(G)$ is the line graph of some graph. Moreover, we characterize finite groups whose order supergraphs are the complement of line graphs.

math.CO↗