COVID-19 is a viral disease that in the form of a pandemic has spread in the entire world, causing a severe impact on people's well being. In fighting against this deadly disease, a pivotal step can prove to be an effective screening and diagnosing step to treat infected patients. This can be made possible through the use of chest X-ray images. Early detection using the chest X-ray images can prove to be a key solution in fighting COVID-19. Many computer-aided diagnostic (CAD) techniques have sprung up to aid radiologists and provide them a secondary suggestion for the same. In this study, we have proposed the notion of Pearson Correlation Coefficient (PCC) along with variance thresholding to optimally reduce the feature space of extracted features from the conventional deep learning architectures, ResNet152 and GoogLeNet. Further, these features are classified using machine learning (ML) predictive classifiers for multi-class classification among COVID-19, Pneumonia and Normal. The proposed model is validated and tested on publicly available COVID-19 and Pneumonia and Normal dataset containing an extensive set of 768 images of COVID-19 with 5216 training images of Pneumonia and Normal patients. Experimental results reveal that the proposed model outperforms other previous related works. While the achieved results are encouraging, further analysis on the COVID-19 images can prove to be more reliable for effective classification.

The exact distance p-power of a graph G, denoted G[#p], is a graph on vertex set V(G) in which two vertices are adjacent if they are at distance exactly p in G. Given integers k and p, we define f(k, p) to be the maximum possible order of a clique in the exact distance p-powers of graphs with maximum degree k + 1. It is easily observed that f(k, 2) ≤ k2 + k + 1. We prove that equality may only hold if a connected component of G is isomorphic to a member of the class Pk of incidence graphs of finite projective k-geometries. (These famous combinatorial structures are known to exist when k is a prime power, and are conjectured not to exist for other values of k.) We then study the case of graphs of maximum degree k + 1 with clique number k2 + k. One way to obtain such a graph is to remove a vertex from a graph in P k; we call Pk' the class of all such resulting graphs. We prove that for any graph G of maximum degree k + 1 whose exact square has a (k2 + k)-clique, either G has a subgraph isomorphic to a graph in P’k, or a connected component of G is a (k + 1)-regular bipartite graph of order 2(k2 + k). We call Ok the class of such bipartite graphs, and study their structural properties. These properties imply that (if they exist) the graphs in Ok must be highly symmetric. Using this structural information, we show that O2 contains only one graph, known as the Franklin graph. We then show that O3 also consists of a single graph, which we build. Furthermore, we show that O4 and O5 are empty. For general values of p, we prove that f(k, p) ≤ (k + 1)k[p/2] + 1, and that the bound is tight for every odd integer p ≥ 3. This implies that f(k, 2) = f(k, 3) whenever there exists a finite projective k-geometry, however, in such a case, the bound of f(k, 3) could also be reached by highly symmetric graphs built from a finite k-geometry, which is not the case for other values of k.