arXiv subjects

Ranveer Singh

Publications and source records attributed to Ranveer Singh.

34 records · Page 2Linked to original sources

arXiv2024

Computing the permanental polynomial of $4k$-intercyclic bipartite graphs

Let $G$ be a bipartite graph with adjacency matrix $A(G)$. The characteristic polynomial $ϕ(G,x)=\det(xI-A(G))$ and the permanental polynomial $π(G,x) = \text{per}(xI-A(G))$ are both graph invariants used to distinguish graphs. For bipartite graphs, we define the modified characteristic polynomial, which is obtained by changing the signs of some of the coefficients of $ϕ(G,x)$. For $4k$-intercyclic bipartite graphs, i.e., those for which the removal of any $4k$-cycle results in a $C_{4k}$-free graph, we provide an expression for $π(G,x)$ in terms of the modified characteristic polynomial of the graph and its subgraphs. Our approach is purely combinatorial in contrast to the Pfaffian orientation method found in the literature to compute the permanental polynomial.

math.CO↗

arXiv2024

Si/AlN p-n heterojunction interfaced with ultrathin SiO2

Ultra-wide bandgap (UWBG) materials hold immense potential for high-power RF electronics and deep ultraviolet photonics. Among these, AlGaN emerges as a promising candidate, offering a tunable bandgap from 3.4 eV (GaN) to 6.1 eV (AlN) and remarkable material characteristics. However, achieving efficient p-type doping in high aluminum composition AlGaN remains a formidable challenge. This study presents an alternative approach to address this issue by fabricating a p+ Si/n-AlN/n+ AlGaN heterojunction structure by following the semiconductor grafting technique. Atomic force microscopy (AFM) analysis revealed that the AlN and the nanomembrane surface exhibited a smooth topography with a roughness of 1.96 nm and 0.545 nm, respectively. High-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) confirmed a sharp and well-defined Si/AlN interface, with minimal defects and strong chemical bonding, crucial for efficient carrier transport. X-ray photoelectron spectroscopy (XPS) measurements demonstrated a type-I heterojunction with a valence band offset of 2.73 eV-2.84 eV and a conduction band offset of 2.22 eV -2.11 eV. The pn diode devices exhibited a linear current-voltage (I-V) characteristic, an ideality factor of 1.92, and a rectification ratio of 3.3E4, with a turn-on voltage of indicating effective p-n heterojunction. Temperature-dependent I-V measurements showed stable operation up to 90 C. The heterojunction's high-quality interface and electrical performance showcase its potential for advanced AlGaN-based optoelectronic and electronic devices.

physics.app-ph↗

arXiv2024

A note on graphs with purely imaginary per-spectrum

In 1983, Borowiecki and Jóźwiak posed the problem ``Characterize those graphs which have purely imaginary per-spectrum.'' This problem is still open. The most general result, although a partial solution, was given in 2004 by Yan and Zhang, who show that if $G$ is a bipartite graph containing no subgraph which is an even subdivision of $K_{2,3}$, then it has purely imaginary per-spectrum. Zhang and Li in 2012 proved that such graphs are planar and admit a Pfaffian orientation. In this article, we describe how to construct graphs with purely imaginary per-spectrum having a subgraph which is an even subdivision of $K_{2,3}$ (planar and nonplanar) using coalescence of rooted graphs.

math.CO↗

arXiv2023

Monocrystalline Si/$β$-Ga$_2$O$_3$ p-n heterojunction diodes fabricated via grafting

The $β$-Ga$_2$O$_3$ has exceptional electronic properties with vast potential in power and RF electronics. Despite the excellent demonstrations of high-performance unipolar devices, the lack of p-type doping in $β$-Ga$_2$O$_3$ has hindered the development of Ga$_2$O$_3$-based bipolar devices. The approach of p-n diodes formed by polycrystalline p-type oxides with n-type $β$-Ga$_2$O$_3$ can face severe challenges in further advancing the $β$-Ga$_2$O$_3$ bipolar devices due to their unfavorable band alignment and the poor p-type oxide crystal quality. In this work, we applied the semiconductor grafting approach to fabricate monocrystalline Si/$β$-Ga$_2$O$_3$ p-n diodes for the first time. With enhanced concentration of oxygen atoms at the interface of Si/$β$-Ga$_2$O$_3$, double side surface passivation was achieved for both Si and $β$-Ga$_2$O$_3$ with an interface Dit value of 1-3 x 1012 /cm2 eV. A Si/$β$-Ga$_2$O$_3$ p-n diode array with high fabrication yield was demonstrated along with a diode rectification of 1.3 x 107 at +/- 2 V, a diode ideality factor of 1.13 and avalanche reverse breakdown characteristics. The diodes C-V shows frequency dispersion-free characteristics from 10 kHz to 2 MHz. Our work has set the foundation toward future development of $β$-Ga$_2$O$_3$-based transistors.

physics.app-ph↗

arXiv2020

Nonsingular Block Graphs: An Open Problem

A block graph is a graph in which every block is a complete graph. Let $G$ be a block graph and let $A(G)$ be its (0,1)-adjacency matrix. Graph $G$ is called nonsingular (singular) if $A(G)$ is nonsingular (singular). An interesting open problem, proposed in 2013 by Bapat and Roy, is to characterize nonsingular block graphs. In this article, we present some classes of nonsingular and singular block graphs and related conjectures.

cs.DM↗

arXiv2020

Accessing low-energy magnetic microstates in symmetry-broken isolated square artificial spin ice vertices with magnetic field

In artificial spin ice systems, an interplay of defects and dipolar interactions is expected to play important roles in stabilizing different collective magnetic states. In this work, we investigated the magnetization reversal of individual defective square artificial spin ice vertices where defects break four-fold rotational symmetry of the system. By varying the angle between the applied field and the geometrical axis of the vertices, we observe a change in energy landscape of the system resulting into the stabilization of collective low-energy magnetic states. We also observe that by changing the angle, it is possible to access different vertex configurations. Micromagnetic simulations are performed for varying angle as well as external field, the results of which are consistent with the experimental data.

cond-mat.mes-hall↗

arXiv2020

Investigating the role of Cu foil orientation in the growth of large BN films synthesized by reactive RF magnetron sputtering

Two dimensional materials are an emerging class of materials which is transforming the present day research activity on a phenomenal scale. Hexagonal boron nitride is a wide band gap 2D material which is an excellent substrate for graphene based electronics. To achieve the full potential of hBN scalable and high yield growth procedures are required. Here, we demonstrate the synthesis of hBN by reactive R.F magnetron sputtering over copper foil. Copper foil preparation conditions determines the phase selectivity of BN films. Deposition of hBN on non-electropolished Cu foils with predominant (100) orientation resulted in growth of BN islands with mixed cubic and hexagonal BN phase. On electropolished Cu foils with high symmetry hexagonal (111) surface termination we get growth of continuous hexagonal BN films, while on Cu foils having (100) and (110) orientation with lower symmetry growth of cubic BN films are observed.

cond-mat.mtrl-sci↗

arXiv2019

Nonsingular (Vertex-Weighted) Block Graphs

A graph $G$ is \emph{nonsingular (singular)} if its adjacency matrix $A(G)$ is nonsingular (singular). In this article, we consider the nonsingularity of block graphs, i.e., graphs in which every block is a clique. Extending the problem, we characterize nonsingular vertex-weighted block graphs in terms of reduced vertex-weighted graphs resulting after successive deletion and contraction of pendant blocks. Special cases where nonsingularity of block graphs may be directly determined are discussed.

cs.DM↗

arXiv2019

Complete multipartite graphs that are determined, up to switching, by their Seidel spectrum

It is known that complete multipartite graphs are determined by their distance spectrum but not by their adjacency spectrum. The Seidel spectrum of a graph $G$ on more than one vertex does not determine the graph, since any graph obtained from $G$ by Seidel switching has the same Seidel spectrum. We consider $G$ to be determined by its Seidel spectrum, up to switching, if any graph with the same spectrum is switching equivalent to a graph isomorphic to $G$. It is shown that any graph which has the same spectrum as a complete $k$-partite graph is switching equivalent to a complete $k$-partite graph, and if the different partition sets sizes are $p_1,\ldots, p_l$, and there are at least three partition sets of each size $p_i$, $i=1,\ldots, l$, then $G$ is determined, up to switching, by its Seidel spectrum. Sufficient conditions for a complete tripartite graph to be determined by its Seidel spectrum are discussed, and a conjecture is made on complete tripartite graphs on more than 18 vertices.

math.CO↗

arXiv2018

Linear time algorithm to check the singularity of block graphs

A block graph is a graph in which every block is a complete graph. Let $G$ be a block graph and let $A(G)$ be its (0,1)-adjacency matrix. Graph $G$ is called nonsingular (singular) if $A(G)$ is nonsingular (singular). Characterizing nonsingular block graphs is an interesting open problem proposed by Bapat and Roy in 2013. In this article, we give a linear time algorithm to check whether a given block graph is singular or not.

cs.DS↗

arXiv2018

Algorithm for $\mathcal{B}$-partitions, parameterized complexity of the matrix determinant and permanent

Every square matrix $A=(a_{uv})\in \mathcal{C}^{n\times n}$ can be represented as a digraph having $n$ vertices. In the digraph, a block (or 2-connected component) is a maximally connected subdigraph that has no cut-vertex. The determinant and the permanent of a matrix can be calculated in terms of the determinant and the permanent of some specific induced subdigraphs of the blocks in the digraph. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Such partitions of the digraph are called the $\mathcal{B}$-partitions. In this paper, first, we develop an algorithm to find the $\mathcal{B}$-partitions. Next, we analyze the parameterized complexity of matrix determinant and permanent, where, the parameters are the sizes of blocks and the number of cut-vertices of the digraph. We give a class of combinations of cut-vertices and block sizes for which the parametrized complexities beat the state of art complexities of the determinant and the permanent.

cs.CC↗

arXiv2018

Rank of weighted digraphs with blocks

Let $G$ be a digraph and $r(G)$ be its rank. Many interesting results on the rank of an undirected graph appear in the literature, but not much information about the rank of a digraph is available. In this article, we study the rank of a digraph using the ranks of its blocks. In particular, we define classes of digraphs, namely $r_2$-digraph, and $r_0$-digraph, for which the rank can be exactly determined in terms of the ranks of subdigraphs of the blocks. Furthermore, the rank of directed trees, simple biblock graphs, and some simple block graphs are studied.

cs.DM↗

arXiv2018

Eigenvalues of weakly balanced signed graphs and graphs with negative cliques

In a signed graph $G$, an induced subgraph is called a negative clique if it is a complete graph and all of its edges are negative. In this paper, we give the characteristic polynomials and the eigenvalues of some signed graphs having negative cliques. This includes cycle graphs, path graphs, complete graphs with vertex-disjoint negative cliques of different orders, and star block graphs with negative cliques. Interestingly, if we reverse the signs of the edges of these graphs, we get the families of weakly balanced signed graphs, thus the eigenvalues of wide classes of weakly balanced signed graphs are also calculated. In social network theory, the eigenvalues of the signed graphs play an important role in determining their stability and developing the measures for the degree of balance.

cs.DM↗

arXiv2017

$\mathcal{B}$-partitions, application to determinant and permanent of graphs

Let $G$ be a graph(directed or undirected) having $k$ number of blocks. A $\mathcal{B}$-partition of $G$ is a partition into $k$ vertex-disjoint subgraph $(\hat{B_1},\hat{B_1},\hdots,\hat{B_k})$ such that $\hat{B}_i$ is induced subgraph of $B_i$ for $i=1,2,\hdots,k.$ The terms $\prod_{i=1}^{k}\det(\hat{B}_i),\ \prod_{i=1}^{k}\text{per}(\hat{B}_i)$ are det-summands and per-summands, respectively, corresponding to the $\mathcal{B}$-partition. The determinant and permanent of a graph having no loops on its cut-vertices is equal to summation of det-summands and per-summands, respectively, corresponding to all possible $\mathcal{B}$-partitions. Thus, in this paper we calculate determinant and permanent of some graphs, which include block graph with negatives cliques, signed unicyclic graph, mix complete graph, negative mix complete graph, and star mix block graphs.

cs.DM↗

arXiv2017

On the Characteristic and Permanent Polynomials of a Matrix

There is a digraph corresponding to every square matrix over $\mathbb{C}$. We generate a recurrence relation using the Laplace expansion to calculate the characteristic, and permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic, and permanent polynomials can be calculated in terms of characteristic, and permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Similar to the characteristic, and permanent polynomials; the determinant, and permanent can also be calculated. Therefore, this article provides a combinatorial meaning of these useful quantities of the matrix theory. We conclude this article with a number of open problems which may be attempted for further research in this direction.

cs.DM↗

arXiv2015

A Complex Network Approach for Collaborative Recommendation

Collaborative filtering (CF) is the most widely used and successful approach for personalized service recommendations. Among the collaborative recommendation approaches, neighborhood based approaches enjoy a huge amount of popularity, due to their simplicity, justifiability, efficiency and stability. Neighborhood based collaborative filtering approach finds K nearest neighbors to an active user or K most similar rated items to the target item for recommendation. Traditional similarity measures use ratings of co-rated items to find similarity between a pair of users. Therefore, traditional similarity measures cannot compute effective neighbors in sparse dataset. In this paper, we propose a two-phase approach, which generates user-user and item-item networks using traditional similarity measures in the first phase. In the second phase, two hybrid approaches HB1, HB2, which utilize structural similarity of both the network for finding K nearest neighbors and K most similar items to a target items are introduced. To show effectiveness of the measures, we compared performances of neighborhood based CFs using state-of-the-art similarity measures with our proposed structural similarity measures based CFs. Recommendation results on a set of real data show that proposed measures based CFs outperform existing measures based CFs in various evaluation metrics.

cs.IR↗