Volume 19 (2023) Issue 1

Abstract: Edge irregular mapping or vertex mapping β : V (U) → {1, 2, 3, …, s} is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wt_β(cd) = β(c)+β(d), ∀c, d ∈ V (U) and cd ∈ E(U). Edge irregularity strength denoted by es(U) is a minimum positive integer used to label vertices to form edge irregular labeling. The aim of this paper is to determine the exact value of edge irregularity strength of different families of snake graph.

Abstract: When ƒ: \((\mathbb{R^n},0)\)→\((\mathbb{R^p},0)\)is a surjective real analytic map with isolated critical value, we prove that the(m)-regularity condition (in a sense we define) ensures that \(\frac{f}{||f||}\) is a fibration on small spheres, ƒ induces afibration on the tubes and these fibrations are equivalent.In particular, we make the statement of [12] more precise in the case of an isolated critical point and weextend it to the case of an isolated critical value.

Abstract: A graph is a tool used to build the interconnection network that a system requires. Such networks inter-operability is ensured by specific labeling. There are several labelings in the literature, however the Group Distance Magic Labeling is better for graphs. A graph G is described as ℋ-distance magic graph if for an abelian group ℋ, there exist one-one mapping 𝓁 between group elements and vertex set of graph G such that ⅀ _{𝓍 ∈ N(u)} 𝓁(x) = µ for all u ∈ V, where µ is the magic constant belongs to abelian group ℋ and N(u) is u′s free neighborhood. In this article, we prove direct product of anti-prism graphs with nth order cycles are ℤ _2st, ℤ₂×ℤ_st, ℤ₃ × ℤ_2t and ℤ₃ × ℤ_{⅔st distance magic graphs.}

Abstract: Non-linear wave equations are created by the elastic wave propagation through inelastic material. We obtain the Lie point symmetries for the non-linear elastic wave equation and the optimal system of the symmetry algebra using Lie symmetry approach. Numerous solutions that are group invariant are obtained under the optimal system of subalgebras of Lie algebra. Additionally, the variational symmetries are obtained via Noether approach and the corresponsing conservation laws are presented. The non-linear elastic wave equation with a damping term is also studied. The local conservation laws using the direct approach are also discussed in this study.

Abstract: The first Zagreb index formulated in its approximate form for -electron energy in 1972 and second Zagreb index formulated in 1975 for branching of molecules. Some modification of these indices was proposed in three different ways naming as novel modification, connection indices and leap Zagreb indices. In this paper we proposed and calculated connection indices for Honey Comb Network and triangular benezoid structures. Furthermore as an extension of our work we also formulated connection indices for line graph of subdivision of Honey Comb and triangular benezoid networks.

Abstract: We study the composition of F. R. Cohen’s map B_n → B_nk with the standard representation of B_nk, where B_n is the braid group on n strings. We prove that the obtained representation of B_n is isomorphic to the direct sum of k copies of the standard representation of B_n. A similar work is done for the welded braid group 𝓌B_n.

Abstract: Consider the Diophantine equation 2^x + 2^y = z², where x, y and z are nonnegative integers. As thisequation has infinitely many solutions, in this paper we study its solutions in case where the unknowns represent Fibonacci and/or Lucas numbers. In other words, we completely resolve the equation in case of (x, y, z) ∈ {(F_i, F_j , F_k),(F_i, F_j ,L_k),(L_i,L_j ,L_k),(L_i,L_j , F_k),(F_i,L_j ,L_k),(F_i,L_j , F_k)} with i, j, k ≥ 1 and F_n and L_n denote the general terms of Fibonacci and Lucas numbers, respectively.

Abstract: Carbon nanotubes are widely used in various fields such as composites, energy devices, electronic applications, and medical applications. The most commonly used nanotubes and nanotubes are V -phenylenic nanotubes and nanotori. Topological analysis of a molecule involves translating its molecular structure into a unique number. In this article, Sombor indices for molecular graph, line graph, and subdivision graph of the V -phenylenic nanotubes and nanotori are calculated.

Abstract: In this article, we study the split equality problem involving nonexpansive semigroup and convex minimization problem. Using a Halpern iterative algorithm, we establish a strong convergence result for approximating a common solution of the aforementioned problems. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We display a numerical example to show the relevance of our result. Our result complements and extends some related results in literature.