MSA: The forgotten index for identifying inappropriate items before computing exploratory item factor analysis

Kaiser’s single-variable measure of sampling adequacy (MSA) is a very useful index for debugging inappropriate items before a factor analysis (FA) solution is fitted to an item-pool dataset for item selection purposes. For reasons discussed in the article, however, MSA is hardly used nowadays in this context. In our view, this is unfortunate. In the present proposal, we first discuss the foundation and rationale of MSA from a ‘modern’ FA view, as well as its usefulness in the item selection process. Second, we embed the index within a robust approach and propose improvements in the preliminary item selection process. Third, we implement the proposal in different statistical programs. Finally, we illustrate its use and advantages with an empirical example in personality measurement.

On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.

Forgotten Index of Generalized Operations on Graphs

In theoretical chemistry, several distance-based, degree-based, and counting polynomial-related topological indices (TIs) are used to investigate the different chemical and structural properties of the molecular graphs. Furtula and Gutman redefined the F -index as the sum of cubes of degrees of the vertices of the molecular graphs to study the different properties of their structure-dependency. In this paper, we compute F -index of generalized sum graphs in terms of various TIs of their factor graphs, where generalized sum graphs are obtained by using four generalized subdivision-related operations and the strong product of graphs. We have analyzed our results through the numerical tables and the graphical presentations for the particular generalized sum graphs constructed with the help of path (alkane) graphs.

Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube

In this article, we provide new formulas to compute the reduced reciprocal randić index, Arithmetic geometric1 index, SK index, SK1 index, SK2 index, edge version of the first zagreb index, sum connectivity index, general sum connectivity index, and the forgotten index using the M-polynomial and finding these topological indices for a boron triangular nanotube. We also elaborate the results with graphical representations.

Some topological properties of uniform subdivision of Sierpiński graphs

Sierpiński graphs are family of fractal nature graphs having applications in mathematics of Tower of Hanoi, topology, computer science, and many more diverse areas of science and technology. This family of graphs can be generated by taking certain number of copies of the same basic graph. A topological index is the number which shows some basic properties of the chemical structures. This article deals with degree based topological indices of uniform subdivision of the generalized Sierpiński graphs S(n,G) and Sierpiński gasket Sn . The closed formulae for the computation of different kinds of Zagreb indices, multiple Zagreb indices, reduced Zagreb indices, augmented Zagreb indices, Narumi-Katayama index, forgotten index, and Zagreb polynomials have been presented for the family of graphs.

New upper bounds for the forgotten index among bicyclic graphs

The forgotten topological index of a graph $G$, denoted by $F(G)$, is defined as the sum of weights $d(u)^{2}+d(v)^{2}$ over all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$. In this paper, we give sharp upper bounds of the F-index (forgotten topological index) over bicyclic graphs, in terms of the order and maximum degree.

The forgotten index of complement graph operations and its applications of molecular graph

A topological index of graph \(G\) is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join \(\overline {G_1+G_2}\), tensor product \(\overline {G_1 \otimes G_2}\), Cartesian product \(\overline {G_1\times G_2}\), composition \(\overline {G_1\circ G_2}\), strong product \(\overline {G_1\ast G_2}\), disjunction \(\overline {G_1\vee G_2}\) and symmetric difference \(\overline {G_1\oplus G_2}\) will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.

Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph

<p>Dutch windmill graph [1, 2] and denoted by <em>Dnm</em>. Order and size of Dutch windmill graph are (<em>n</em>−1)<em>m</em>+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, <em>M</em>-polynomials and some topological indices in term of the <em>M</em>-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.</p>

Some Topological Indices and their Polynomials of Graphene

In this manuscript we have computed third Zagreb index, first Zagreb polynomial, second Zagreb polynomial, third Zagreb polynomial, hyper Zagreb polynomial, forgotten index, forgotten polynomial, symmetric division index and symmetric division polynomial of Graphene. These quantities are based on degrees of the vertices.

COMPUTING TOPOLOGICAL INDICES OF SiO2 LAYER STRUCTURE AND BENZENOID SERIES

A molecular graph can be transformed using map operations, one of these, named Capra, being defined by Diudea (2005). Topological indices are closely related to the toxicological, physicochemical, pharmacological properties of a chemical compound. These topological indices correlate certain physico-chemical properties like boiling point, stability and strain energy of chemical compounds. In this paper, we focus on the Silicate SiO2 layer structure and the structure of Capra-designed planar benzenoid series , (). We determined Zagreb type indices, Forgotten index, Augmented index and Balaban index for these structures.