Journal of Prime Research in Mathematics

Abstract: Let f be a function from the vertex set \(V (G)\) to \({0, 1, 2}\). For each edge \(uv\) assign the label \(\frac{f(u)+f(v)}{2}\). \(f\) is called a mean cordial labeling if \(|v_f (i) − v_f (j)| ≤ 1\) and \(|e_f (i) − e_f (j)| ≤ 1\), \(i, j ∈ {0, 1, 2}\), where \(v_f (x)\) and \(e_f (x)\) respectively denote the number of vertices and edges labeled with \(x\) \((x = 0, 1, 2)\). A graph with a mean cordial labeling is called a mean cordial graph. In this paper we investigate mean cordial labeling behavior of prism, \(K_2 +\overline{K_m}\), \(K_n + \overline{2K_2}\), book \(B_m\) and some snake graphs.

Abstract: Lanczos-type algorithms are mostly derived using recurrence relationships between formal orthogonal polynomials. Various recurrence relations between these polynomials can be used for this purpose. In this paper, we discuss recurrence relations A19 and B6 for the choice \(U_i(x) = P_{i}^{(1)}\), where \(U_i\) is an auxiliary family of polynomials of exact degree \(i\). This leads to new Lanczos-type algorithm \(A_19/B_6\) that shows superior stability when compared to existing algorithms of the same type. This new algorithm is derived and described here. Computational results obtained with it are compared to those of the most robust algorithms of this type namely \(A_12\),  (A^{new}_12\) \(A_5/B_{10}\) and \(A_8/B_{10}\) on the same test problems. These results are included.

Abstract: This paper presents the heat transfer of a third grade fluid between two heated parallel plates for two models: constant viscosity model and Reynold’s model. In both cases the nonlinear energy and momentum equations have been solved by HAM. The graphs for the velocity and temperature profiles are plotted and discussed for various values of the emerging parameters in the problem. The main effect is governed by whether or not the fluid is non-Newtonian and the temperature effects are being referred to have a less dominant role.

Abstract: In this paper we introduce the notion of \((λ, µ)\)-Fuzzy ternary subsemirings and \((λ, µ)\)-Fuzzy ideals in ternary semirings which can be regarded as the generalization of fuzzy ternary subsemirings and fuzzy ideals in ternary semirings.

Abstract: We are investigating the multiplication group of a special class of quasigroup called AG-group. We prove some interesting results such as: The multiplication group of an AG-group of order n is a non-abelian group of order 2n and its left section is an abelian group of order n. The inner mapping group of an AG-group of any order is a cyclic group of order 2.

Abstract: Let \(C\) be a configuration of pebbles on a graph \(G\). A pebbling move (step) consists of removing two pebbles from one vertex, throwing one pebble away, and moving the other pebble to an adjacent vertex. The \(t\)-pebbling number, \(f_t(G)\), of a connected graph \(G\), is the smallest positive integer such that from every configuration of \(f_t(G)\) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number for squares of cycles.