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The pairwise balanced designs (PBD's) is a pair (P;B), where P is a finite set of v points and B is a family of subsets of P, called blocks such that every two distinct points in P appear in exactly one block. Let α(G) = α and β(G) = β be the vertex covering and independence number of a graph G = (V;E) with the minimum and maximum cardinality of such sets are denoted by α-sets and β-sets of G, respectively (or, simply (α; β)-sets). In this paper, we obtain the total number of (α; β)-sets in different jump sizes of some circulant graphs apart from strongly regular graphs which are the blocks of PBD. [ABSTRACT FROM AUTHOR]

Image thresholding is the classical problem in the area of image processing. The noise of the image usually assume to be Gaussian can be removed using threshold methods, without disturbing the significant features of the image. One of the important features of the image is its edge contour, which is well illustrated by the ability to recognize objects from the drawing that only outlines edges. In this article, we introduced a novel threshold value used to estimate the true image from its noisy counterpart that considerably avoids the loss of edge contour. The standard of the image has been derived by peak signal to noise ratio (psnr) and investigate with the established threshold parameters. [ABSTRACT FROM AUTHOR]

Image thresholding is the classical problem in the area of image processing. The noise of the image usually assume to be Gaussian can be removed using threshold methods, without disturbing the significant features of the image. One of the important features of the image is its edge contour, which is well illustrated by the ability to recognize objects from the drawing that only outlines edges. In this article, we introduced a novel threshold value used to estimate the true image from its noisy counterpart that considerably avoids the loss of edge contour. The standard of the image has been derived by peak signal to noise ratio (psnr) and investigate with the established threshold parameters. [ABSTRACT FROM AUTHOR]

However, the Latin square (LS) designs have been studied extensively with some classes of regular graphs, and their connections with classical graph parameters were not explored. This article determines the existence and non-existence of the Latin square designs with two association schemes. Also, discusses the uniqueness of the polynomials obtained from the matrices of the associates of LS-designs emerging from the total number of minimum covering, maximum independent, and minimum dominating sets of certain classes of regular graphs such as Hypercube, Paley graph, Torus graph, Clebsch graph, Shrikhande graph. Further, we generalized the parameters of LS-designs of Circulant graphs, Complete multipartite graphs, and some Nilpotent Cayley graphs. [ABSTRACT FROM AUTHOR]

A set S ⊆ V of a graph G = (V, E) is a Neighborhood set of G if G = S v∈S hN(v)i, where hN(v)i is the subgraph induced by v and all vertices adjacent to v. The neighborhood number, η(G) is the minimum cardinality of a neighborhood set of G. The minimum neighborhood set S with |S| = η(G) is called η-set. Generally, the partially balanced incomplete block(PBIB)-Designs are obtained from the family of strongly regular graphs. Surprisingly, in this paper we obtain the PBIB-Designs and m-association schemes for 1 ≤ m ≤ b p 2 c arising from η -sets of certain jump sizes of circulant graphs. [ABSTRACT FROM AUTHOR]