arXiv subjects

Sandeep Dalal

Publications and source records attributed to Sandeep Dalal.

14 recordsLinked to original sources

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↗

arXiv2023

Spectrum of conjugacy and order super commuting graphs of some finite groups

Let $Γ$ be a simple finite graph with vertex set $V(Γ)$ and edge set $E(Γ)$. Let $\mathcal{R}$ be an equivalence relation on $V(Γ)$. The $\mathcal{R}$-super $Γ$ graph $Γ^{\mathcal{R}}$ is a simple graph with vertex set $V(Γ)$ and two distinct vertices are adjacent if either they are in the same $\mathcal{R}$-equivalence class or there are elements in their respective $\mathcal{R}$-equivalence classes that are adjacent in the original graph $Γ$. We first show that $Γ^{\mathcal{R}}$ is a generalized join of some complete graphs and using this we obtain the adjacency and Laplacian spectrum of conjugacy and order super commuting graphs of dihedral group $D_{2n}\; (n\geq 3)$, generalized quaternion group $Q_{4m} \;(m\geq 2)$ and the nonabelian group $\mathbb Z_p \rtimes \mathbb Z_q$ of order $pq$, where $p$ and $q$ are distinct primes with $q|p-1$.

math.GR↗

arXiv2022

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

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 $G$. The $B$ super $A$ graph is a simple graph with vertex set $G$ and two vertices are adjacent if either they are in the same $B$-equivalence class or there are elements in their $B$-equivalence classes that are adjacent in the original $A$ graph. The graph obtained by deleting the dominant vertices (adjacent to all other vertices) from a $B$ super $A$ graph is called the reduced $B$ super $A$ graph. In this article, for some pairs of $B$ super $A$ graphs, we characterize the finite groups for which a pair of graphs are equal. We also characterize the dominant vertices for the order super commuting graph $Δ^o(G)$ of $G$ and prove that for $n\geq 4$ the identity element is the only dominant vertex of $Δ^o(S_n)$ and $Δ^o(A_n)$. We characterize the values of $n$ for which the reduced order super commuting graph $Δ^o(S_n)^*$ of $S_n$ and the reduced order super commuting graph $Δ^o(A_n)^*$ of $A_n$ are connected. We also prove that if $Δ^o(S_n)^*$ (or $Δ^o(A_n)^*$) is connected then the diameter is at most $3$ and shown that the diameter is $3$ for many value of $n.$

math.GR↗

arXiv2022

Lambda Number of the enhanced power graph of a finite group

The enhanced power graph of a finite group $G$ is the simple undirected graph whose vertex set is $G$ and two distinct vertices $x, y$ are adjacent if $x, y \in \langle z \rangle$ for some $z \in G$. An $L( 2,1)$-labeling of graph $Γ$ is an integer labeling of $V(Γ)$ such that adjacent vertices have labels that differ by at least $2$ and vertices distance $2$ apart have labels that differ by at least $1$. The $λ$-number of $Γ$, denoted by $λ(Γ)$, is the minimum range over all $L( 2,1)$-labelings. In this article, we study the lambda number of the enhanced power graph $\mathcal{P}_E(G)$ of the group $G$. This paper extends the corresponding results, obtained in [22], of the lambda number of power graphs to enhanced power graphs. Moreover, for a non-trivial simple group $G$ of order $n$, we prove that $λ(\mathcal{P}_E(G)) = n$ if and only if $G$ is not a cyclic group of order $n\geq 3$. Finally, we compute the exact value of $λ(\mathcal{P}_E(G))$ if $G$ is a finite nilpotent group.

math.GR↗

arXiv2021

The cyclic graph of a semigroup

The cyclic graph $Γ(S)$ of a semigroup $S$ is the simple graph whose vertex set is $S$ and two vertices $x, y$ are adjacent if the subsemigroup generated by $x$ and $y$ is monogenic. In this paper, we classify the semigroup $S$ such that whose cyclic graph $Γ(S)$ is complete, bipartite, tree, regular and a null graph, respectively. Further, we determine the clique number of $Γ(S)$ for an arbitrary semigroup $S$. We obtain the independence number of $Γ(S)$ if $S$ is a finite monogenic semigroup. At the final part of this paper, we give bounds for independence number of $Γ(S)$ if $S$ is a semigroup of bounded exponent and we also characterize the semigroups attaining the bounds.

math.GR↗

arXiv2021

Enhanced Power Graph of Certain Non-abelian Groups

The enhanced power graph of a group $G$ is a simple undirected graph with vertex set $G$ and two vertices are adjacent if they belong to same cyclic subgroup. In this paper, we study distant properties and detour distant properties such as closure, interior, distance degree sequence and eccentric subgraph of the enhanced power graph of semidihedral group. Consequently, we obtained the metric dimension and resolving polynomial of the enhanced power graph of semidihedral group. At the final part of this paper, we obtained the Laplacian spectrum of the enhanced power graph of semidihedral, dihedral and generalized quaternion groups.

math.GR↗

arXiv2021

On The Enhanced Power Graph of a Semigroup

The enhanced power graph $\mathcal P_e(S)$ of a semigroup $S$ is a simple graph whose vertex set is $S$ and two vertices $x,y \in S$ are adjacent if and only if $x, y \in \langle z \rangle$ for some $z \in S$, where $\langle z \rangle$ is the subsemigroup generated by $z$. In this paper, first we described the structure of $\mathcal P_e(S)$ for an arbitrary semigroup $S$. Consequently, we discussed the connectedness of $\mathcal P_e(S)$. Further, we characterized the semigroup $S$ such that $\mathcal P_e(S)$ is complete, bipartite, regular, tree and null graph, respectively. Also, we have investigated the planarity together with the minimum degree and independence number of $\mathcal P_e(S)$. The chromatic number of a spanning subgraph, viz. the cyclic graph, of $\mathcal P_e(S)$ is proved to be countable. At the final part of this paper, we construct an example of a semigroup $S$ such that the chromatic number of $\mathcal P_e(S)$ need not be countable.

math.GR↗

arXiv2021

Deep Learning to Quantify Pulmonary Edema in Chest Radiographs

Purpose: To develop a machine learning model to classify the severity grades of pulmonary edema on chest radiographs. Materials and Methods: In this retrospective study, 369,071 chest radiographs and associated radiology reports from 64,581 (mean age, 51.71; 54.51% women) patients from the MIMIC-CXR chest radiograph dataset were included. This dataset was split into patients with and without congestive heart failure (CHF). Pulmonary edema severity labels from the associated radiology reports were extracted from patients with CHF as four different ordinal levels: 0, no edema; 1, vascular congestion; 2, interstitial edema; and 3, alveolar edema. Deep learning models were developed using two approaches: a semi-supervised model using a variational autoencoder and a pre-trained supervised learning model using a dense neural network. Receiver operating characteristic curve analysis was performed on both models. Results: The area under the receiver operating characteristic curve (AUC) for differentiating alveolar edema from no edema was 0.99 for the semi-supervised model and 0.87 for the pre-trained models. Performance of the algorithm was inversely related to the difficulty in categorizing milder states of pulmonary edema (shown as AUCs for semi-supervised model and pre-trained model, respectively): 2 versus 0, 0.88 and 0.81; 1 versus 0, 0.79 and 0.66; 3 versus 1, 0.93 and 0.82; 2 versus 1, 0.69 and 0.73; and, 3 versus 2, 0.88 and 0.63. Conclusion: Deep learning models were trained on a large chest radiograph dataset and could grade the severity of pulmonary edema on chest radiographs with high performance.

eess.IV↗

arXiv2020

On the commuting graphs of Brandt semigroups

The commuting graph of a finite non-commutative semigroup S, denoted by Δ(S), is the simple graph whose vertices are the non-central elements of S and two distinct vertices x; y are adjacent if xy = yx. In the present paper, we study various graph-theoretic properties of the commuting graph Δ(B_n) of Brandt semigroup B_n including its diameter, clique number, chromatic number, independence number, strong metric dimension and dominance number. Moreover, we obtain the automorphism group Aut(Δ(Bn)) and the endomorphism monoid End(Δ(Bn)) of Δ(Bn). We show that Aut(Δ(Bn)) = S_n \times Z_2, where S_n is the symmetric group of degree n and Z_2 is the additive group of integers modulo 2. Further, for n \geq 4, we prove that End(Δ(Bn)) =Aut(Δ(Bn)). In order to provide an answer to the question posed in [2], we ascertained a class of inverse semigroups whose commuting graph is Hamiltonian.

math.GR↗

arXiv2020

On The Commuting Graph of Semidihedral Group

The commuting graph $Δ(G)$ of a finite non-abelian group $G$ is a simple graph with vertex set $G$ and two distinct vertices $x, y$ are adjacent if $xy = yx$. In this paper, among some properties of $Δ(G)$, we investigate $Δ(SD_{8n})$ the commuting graph of the semidihedral group $SD_{8n}$. In this connection, we discuss various graph invariants of $Δ(SD_{8n})$ including minimum degree, vertex connectivity, independence number, matching number and detour properties. We also obtain the Laplacian spectrum, metric dimension and resolving polynomial of $Δ(SD_{8n})$.

math.GR↗

arXiv2020

Equality of various graphs on finite semigroups

In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the graphs in this pair are equal. In this connection, for each of the graph we also give a necessary and sufficient condition on $S$ such that it is complete. The work of this paper generalize the corresponding results obtained for groups.

math.GR↗

arXiv2020

Structural, transport, optical and electronic properties of Sr$_2$CoNbO$_6$ thin films

We study the effect of substrate induced strain on the structural, transport, optical and electronic properties of Sr$_2$CoNbO$_6$ double perovskite thin films. The reciprocal space mapping, $ϕ$-scan and high-resolution $θ$-2$θ$ scans of x-ray diffraction patterns suggest the epitaxial nature and high-quality of the films deposited on various single crystal ceramic substrates. A systematic enhancement in the dc electronic conductivity is observed with increase in the compressive strain, while a sharp reduction in case of tensile strain, which are further supported by change in the activation energy and density of states near the Fermi level. The optical band gap extracted from two distinct absorption bands, observed in the visible-near infrared spectroscopy show a non-monotonic behavior in case of compressive strain while significant enhancement with tensile strain. Unlike the bulk Sr$_2$CoNbO$_6$ (Co$^{3+}$ and Nb$^{5+}$), we observe different valence states of Co namely 2+, 3+ and 4+, and tetravalent Nb (4$d^1$) in the x-ray photoemission spectroscopy measurements. Moreover, a reduction in the average oxygen valency with the compressive strain due to enhancement in the covalent character of Co/Nb--O bond is evident. Interestingly, we observe sharp Raman active modes in these thin films, which indicates a significant enhancement in structural ordering as compared to the bulk.

cond-mat.mtrl-sci↗

arXiv2020

Structural and transport properties of La$_{1-x}$Sr$_x$Co$_{1-y}$Nb$_y$O$_3$ thin films

We present the structural and transport properties of La$_{1-x}$Sr$_x$Co$_{1-y}$Nb$_y$O$_3$ ($y=$ 0.1 and $x=$ 0; $y=$ 0.15 and $x=$ 0.3) thin films grown on (001) orientated single crystalline ceramic substrates to investigate the effect of lattice induced compressive and tensile strain. The high resolution x-ray diffraction measurements, including $θ$-2$θ$ scan, $Φ$-scan, and reciprocal space mapping, affirm single phase; four-fold symmetry; good quality of deposited thin films. The atomic force micrographs confirm that these films have small root mean square roughness in the range of $\sim$0.5--7~nm. We observed additional Raman active modes in the films owing to the lowered crystal symmetry as compared to the bulk. More interestingly, the temperature dependent dc-resistivity measurements reveal that films become insulating due to induced lattice strain in comparison to bulk, however for the larger compressive strained films conductivity increase significantly owing to the higher degree of $p-d$ hybridization and reduction in bandwidth near the Fermi level.

cond-mat.mtrl-sci↗

arXiv2019

Semi-supervised Learning for Quantification of Pulmonary Edema in Chest X-Ray Images

We propose and demonstrate machine learning algorithms to assess the severity of pulmonary edema in chest x-ray images of congestive heart failure patients. Accurate assessment of pulmonary edema in heart failure is critical when making treatment and disposition decisions. Our work is grounded in a large-scale clinical dataset of over 300,000 x-ray images with associated radiology reports. While edema severity labels can be extracted unambiguously from a small fraction of the radiology reports, accurate annotation is challenging in most cases. To take advantage of the unlabeled images, we develop a Bayesian model that includes a variational auto-encoder for learning a latent representation from the entire image set trained jointly with a regressor that employs this representation for predicting pulmonary edema severity. Our experimental results suggest that modeling the distribution of images jointly with the limited labels improves the accuracy of pulmonary edema scoring compared to a strictly supervised approach. To the best of our knowledge, this is the first attempt to employ machine learning algorithms to automatically and quantitatively assess the severity of pulmonary edema in chest x-ray images.

cs.CV↗