This paper discusses optical soliton solutions for the paraxial wave model (PWM) in Kerr law media. Mathematically, PWM a monochromatic beam is equivalent to Schrödinger equation of free quantum particle. The ϕ6 expansion technique used obtain dark, bright, singular, bright-dark combined and periodic solitons. obtained by this method are form trigonometric, hyperbolic, exponential functions. To prompt important propagated structures, some scrutinized demonstrated 3D, contour, 2D plots using...

Several chemical and medical experimentation reveals a dependence of physicochemical biological properties compound on its molecular structure. Molecular/topological descriptors/indices retrieve this by employing mathematical/statistical tools to generate quantitative structure property/activity relationship (QSAR/QSPR) models. QSAR/QSPR models are regression which theoretically relate physicochemical/biological property descriptor. By converting graph, graph-theoretic topological indices...

In this paper, we give sharp bounds of the Hankel determinant H2(3)(f) for coefficients functions in class starlike related to a domain that is like three leaves. We also determinants H3(1)(f) and convex three-leaf-like domain.

Structure-based topological descriptors of chemical networks enable us the prediction physico-chemical properties and bioactivities compounds through QSAR/QSPR methods. Topological indices are numerical values to represent a graph which characterises graph. One latest distance-based index is Mostar index. In this paper, we study index, Szeged PI <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mtext>ABC</mtext></mrow><mrow><mtext>GG</mtext></mrow></msub></math>...

The q-rung picture fuzzy sets act as a proficient and extensive extension of orthopair within set theory. parameter q the three real-valued membership functions enable us to perform better than existing approaches in describing mysterious data. Here, we built aggregation operators for q-RPLFS framework using Schweizer Sklar (SS) operations. We introduced analyzed several kinds detail, including linguistic SS weighted averaging operator (q-RPLSSAO) geometric (q-RPLSSGO). solving MADM problems...

The neutrosophic hesitant fuzzy set is the union of and in which each element has membership, neutrality, non-membership arrays verifies infrequency labeling uncertainty daily usage. We proposed two novel operators this analysis that demonstrate evolution, one partitioned Maclaurin symmetric mean (NHFPMSM) other weighted (NHFWPMSM). These novels aim to draw inspiration from concept. diverse properties special cases these are demonstrated article. introduce a multiple-criteria decision-making...

In this paper, we determine the efficiency of all commonly occurring eigenvalues‐based topological descriptors for measuring π ‐electronic energy lower polycyclic aromatic hydrocarbons. Results show some favorable outcomes as spectrum‐based such adjacency energy, arithmetic‐geometric geometric‐arithmetic and Estrada index have best correlation coefficients greater than 0.999 among others. However, certain well‐known adjacency, Laplacian &amp; signless spectral radii, first second Zagreb...

There are numeric numbers that define chemical descriptors represent the entire structure of a graph, which contain basic structure. Of these, main factors topological indices such they related to different physical properties primary compounds. The biological activity compounds can be constructed by help indices. In theoretical chemistry, numerous have been invented, as Zagreb index, Randić Wiener and many more. Hex-derived networks an assortment valuable applications in drug store,...

Topological indices are quantitative measurements that describe a molecule’s topology and quantified from the graphical representation. The significance of topological is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between particular molecular or biological activity one several biochemical and/or structural features QSPRs (quantitative structure‐property relationships) QSARs structure‐activity relationships). In this paper, we give explicit...

Abstract Recently, increasing attention has been paid to The Optical Transpose Interconnection System (OTIS) network because of its prospective applications in architectures for parallel as well distributed systems [27, 28]. Different interconnection networks the context topological indices are researched recently [25, 26]. This article includes computions general Randi´c, first and second Zagreb, sum connectivity, multiple zagreb, hyper ABC GA OTIS (swapped biswapped) by taking path k...

In chemical graph theory, a topological index is numerical representation of network, while descriptor correlates certain physicochemical characteristics underlying compounds besides its representation. The plays vital role in modeling and designing any network. Simonraj et al. derived new type graphs, which named third hex-derived networks. our work, we discuss the networks H D N 3 ( r ) , T R C compute exact results for indices are based on degrees end vertices.

AbstractPhenylenes belong to a special class of conjugated hydrocarbons composed arrangement hexagons and squares. In the phenylene structure, every square is adjacent pair hexagons, any two are not adjacent. If in structure only squares hexagon, then it called chain. this paper, we compute expected values first second Gourava index, redefined Zagreb Hyper-Zagreb index random chains. Furthermore, comparison between computed indices among classes chains has been investigated.GRAPHICAL...

The cubic intuitionistic fuzzy set is an expansion of the that displays massive information to demonstrate interval-valued sets and sets. This increment informs limitations essential in existing frameworks, primarily focusing on significance embracing our access for more accurate decisions compound unresolved structures. Schweizer Sklar (SS) operations are engaged promoting strong aggregation operators through this research. Operators such as power weighted average (CIFSSPWA) geometric...

The present-day trend of the numerical coding chemical structures with topological indices (TIs) has established quite successful in medicinal chemistry and bioinformatics. This strategy provides annotation, comparison, rapid collection, mining, retrieval within large databases. Afterward, TIs can be used to look for quantitative structure-activity relationships structure-property relationships, which are models that associate structure biological activity. In these analyses, degree-based...

In theoretical chemistry, the numerical parameters that are used to characterize molecular topology of graphs called topological indices. Several physical and chemical properties like boiling point, entropy, heat formation, vaporization enthalpy compounds can be determined through these Graph theory has a considerable use in evaluating relation various indices some derived graphs. this article, we will compute Randić, first Zagreb, harmonic, augmented atom-bond connectivity,...

In quantitative structure property (QSPR) and activity (QSAR) relationships studies, topological indices are utilized to associate the biological of underline structures with their physical properties like strain energy, distortion, melting point, boiling stability, etc. these degree based have obtained center position between various kind descriptors, due simplicity finding rapidity which estimations can be accomplished. this paper, we compute general Randic, first second Zagreb, Atom Bond...

A graph’s entropy is a functional one, based on both the graph itself and distribution of probability its vertex set. In theory information, has origins. Hex‐derived networks have variety important applications in medication store, hardware, system administration. this article, we discuss hex‐derived network type 1 2, written as HDN 1( n ) 2( ), respectively order . We also compute some degree‐based entropies such Randić, ABC, G ).

Topological indices are numerical numbers that represent the topology of a molecule and calculated from graphical depiction molecule. The importance topological is due to their use as descriptors in QSPR/QSAR modeling. QSPRs (quantitative structure-property relationships) QSARs structure-activity mathematical correlations between specified molecular property or biological activity one more physicochemical and/or structural properties. In this paper, we give explicit expressions some...

Let S(m,e) be a class of numerical semigroups with multiplicity m and embedding dimension e. We call graph GS an S(m,e)-graph if there exists semigroup S∈S(m,e) V(GS)={x:x∈g(S)} E(GS)={xy⇔x+y∈S}, where g(S) denotes the gap set S. The aim this article is to discuss planarity S(m,e)-graphs for some cases S irreducible semigroup.

In this paper, we give the characterization of unmixed f-ideals degree d ≥ 2 generalizing results given in [1 Abbasi , G. Q. Ahmad S. Anwar I. Baig W. A. ( 2012 ). f-Ideals 2. Algebra Colloquium 19 (Spec 1):921–926 . [Google Scholar]].

In this paper, we introduce the concept of [Formula: see text]-simplicial complexes by generalizing term text]-graphs (introduced in [H. Mahmood, I. Anwar and M. K. Zafar, Construction Cohen–Macaualy text]-graphs, J. Algebra Appl. 13(6) (2014) 1450012]). particular, discuss problem connectedness pure complexes. Moreover, give a complete characterization connected disconnected classification all text]-graphs.

A graph’s entropy is a functional one, based on both the graph itself and distribution of probability its vertex set. In theory information, has origins. Dominating David derived networks have variety important applications in medication store, hardware, system administration. this study, we discuss dominating network type 1, 2, 3 written as D 1 ( n ), 2 respectively order . We also compute some degree‐based entropies such Randić, B C , GA ).

A subset S of non-negative integers No is called a numerical semigroup if it submonoid and has finite complement in No. An undirected graph G(S) associated with having V(G(S))={vi:i∈No∖S} E(G(S))={vivj⇔i+j∈S}. In this article, we propose conjecture for the clique number graphs symmetric family semigroups arbitrary multiplicity embedding dimension. Furthermore, prove case dimension 7.

A subset Δ of non-negative integers N0 is called a numerical semigroup if it submonoid and has finite complement in N0. graph GΔ Δ(α,β)-graph there exists with multiplicity α embedding dimension β such that V(GΔ)={vi:i∈N0∖Δ} E(GΔ)={vivj⇔i+j∈Δ}. In this article, we compute the Δ(α,β)-graphs for irreducible Arf semigroups having metric 2. It proved be an arf then are exactly 2 8 non-isomorphic respectively, whose