Journal of Prime Research in Mathematics

Abstract: Liu et al. [IEEE Access; 7(2019); 105479-105488] defined the concept of the generalized subdivided operations on graphs and obtained the generalized F-sum graphs. They also calculated the 1st and 2nd Zagreb indices of the generalized F-sum graphs. In the continuation of this work, we study the forgotten index (F-index) of the generalized F-sum graphs in terms of different topological indices (TI’s) of their base graphs. In the end, the results of F-index on the generalized F-sum graphs acquired by the particular classes of alkane are also included.

Abstract: A sum divisor cordial labeling of a graph \(G\) with vertex set \(V\) is a bijection \(f\) from \(V\) to \(\{1, 2, ··· , |V (G)|\}\) such that an edge \(uv\) is assigned the label 1 if 2 divides \(f(u) + f(v)\) and \(0\) otherwise; and the number of edges labeled with \(0\) and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that \(P^{2}_{n}, P_n ⊙ mK_1, S(P_n ⊙ mK_1), D_2(P_n), T(P_n)\), the graph obtained by duplication of each vertex of path by an edge, \(T(C_n), D_2(C_n)\), the graph obtained by duplication of each vertex of cycle by an edge, C^{(t)}_{4}, book, quadrilateral snake and alternate triangular snake are sum divisor cordial graphs.

Abstract: The concept of picture hesitant fuzzy set (PHFS) is a generalization of picture fuzzy set (PFS) and hesitant fuzzy set (HFS). Such kind of idea can be very helpful in problems where opinions are of more than two types i.e. yes, no, abstinence and refusal. The goal of this manuscript is to introduce the concept of similarity measures for PHFSs as a generalization of the similarity measures for PFS. We studied the basic concepts of  PFSs, HFSs and PHFSs. We proposed some similarity measures for PHFSs such as cosine similarity measure, set-theoretic similarity measure and grey similarity measure for PHFSs. Some weighted similarity measures are also proposed where weight of the attributes is considered. Then these similarity measures for PHFSs are applied to a building material recognition problem. Finally, a comparative study of similarity measures of PHFSs is established with similarity measures of PFSs, HFSs, IFSs and IHFSs and the advantages of new work are studied.

Abstract: The main focus of this article is to investigate the exact solution for MHD flow of Maxwell fluid over an infinite vertical plate with ramped temperature and constant concentration. Plate is moving along a straight line with arbitrary velocity which depends on time. Laplace transform and convolution theorem are used to acquire solutions for temperature, concentration and velocity. Moreover, results already present in literature are acquired as limiting case from these general results.

Abstract: In this paper, we establish some results for functions whose derivatives in absolute values at certain power is generalized \((α, m)\)-convex function. We derive some new estimates to the right-hand side of HermiteHadamard inequality for functions whose absolute values of second derivatives raised to real powers are m-convex functions. Special cases are discussed as applications of our results. The technique of this paper may stimulate further research in this field.

Abstract: In this paper we introduce a new comprehensive six-parameter distribution called the modified beta generalized linear failure rate distribution. One of the interest of this distribution is to generalize some well-known flexible distributions discussed in the literature, such as (i) the beta linear failure rate distribution, (ii) the generalized linear failure rate distribution, (iii) the beta exponential distribution, (iv) the beta Rayleigh distribution and (v) the generalized exponential distribution, among others. We derive some of its statistical properties, including the moments, the moment generating function, the quantile function, the order statistics and the mean deviations. We propose the method of maximum likelihood for estimating the model parameters. A simulation study is performed in order to investigate the performance of the maximum likelihood estimators. A real data set is used to illustrate the importance and the flexibility of the new distribution.