Subgraphs Generating Wheels and Fans of Some Orders
Ma. Theresa Christine C. Valdez1 and Severino V. Gervacio2
1Mathematics and Statistics Department, De La Salle University- Dasmariñas, City of Dasmariñas, Cavite, Philippines
2Mathematics and Statistics Department, De La Salle University, Manila, Philippines
ABSTRACT
Several studies have been initiated separately about finding the generator subgraphs of different classes of graphs including cycles, stars, paths, complete bipartite and complete graphs. The results of this work contribute to this wider study by identifying generator subgraphs of wheels and fans. As a preliminary study, this paper started with working on wheels and fans of small orders in terms of vertices and edges of these kinds of graphs. A subgraph H of the wheel or of the fan was tested if it generates its edge space denoted E (G) by identifying all the elements of EH(G)={A| A∈E (G), ≅ H} where is the subgraph of G isomorphic to H formed by the edges in A. Then it was shown that every element in E (G) is expressible as a linear combination of some elements in EH(G). It was found that paths of order 4, denoted by P4 is a generator subgraph of wheels and fans and that most of their subgraphs having an odd number of edges are also generator subgraphs.
Keywords: cardinality, edge space, edge-set, isomorphic graph, path, span
Generating Small Area Estimates of Poverty Incidence in Region IV-A (CALABARZON)
Nelda Atibagos Nacion
De La Salle University- Dasmariñas, City of Dasmariñas, Cavite, Philippines
ABSTRACT
The main purpose of this study is to propose an alternative procedure in the generation of small area estimates of poverty incidence using imputation-like procedures coupled with a calibration of estimates to ensure coherence in the regional estimates. This study used the Family Income and Expenditure Survey of 2009 and the Census of Population and Housing (CPH form 2) 2010 to come up with reliable estimates of poverty incidence by municipal level. Since CPH is conducted in the Philippines every 10 years, CPH 2010 is the latest data that was used. The researcher was able to produce small area estimates of poverty in Region IV-A (CALABARZON) at municipal level by combining survey data with auxiliary data derived from census. CALABARZON was chosen even if this region is not really poor in general, but the researcher believes that poverty is still evident in smaller areas especially at the municipal level. The study fitted different models. By comparing the methods of imputation, it was found that the Stochastic Regression Imputation performed better in attaching the income in census. The error used in Stochastic Regression was estimated using non-parametric method called Kernel Density Estimation.
Keywords: poverty; small area estimation; imputation; calibration; stochastic regression imputation
Exploring Mathematical Concepts in Artifacts from Museo De La Salle
Edwin S. Bunag, Lea D. Maderal, and Ma. Theresa Christine C. Valdez
Mathematics and Statistics Department, De La Salle University- Dasmariñas, City of Dasmariñas, Cavite, Philippines
ABSTRACT
Artifacts preserved at the Museo De La Salle were explored to identify mathematical concepts and to know whether these could serve as manipulatives for teaching K-12 students particularly from Grade 7 to Grade 10. A survey and key informant interviews were conducted among seven (7) mathematics teachers in order to explore the mathematical concepts that are observable in 100 randomly selected artifacts. The study found that Measurement, Patterns and Algebra and Geometry were the main concepts that were evident and can be learned from these artifacts. The teachers were also queried on how these mathematical concepts can be explored and learned by the students. Results revealed that these concepts can be explored and learned through visual approach, classification, measurement, and utilizing it as concrete exemplars for real-life situational problems. The study also emphasized that museums are potential resources for the teaching and learning of Mathematics among K-12 students while also promoting awareness, preservation, and appreciation of the arts and culture.
Keywords: K-12 students, manipulatives, mathematics, museum, measurement
New Classes of Perfect Totient Numbers
Jovele Baccay1 and Leonor Ruivivar2
1Mathematics and Statistics Department, De La Salle University- Dasmariñas, City of Dasmariñas, Cavite, Philippines
2Mathematics and Statistics Department, De La Salle University, Manila, Philippines
ABSTRACT
n this paper, we present a self-contained discussion of perfect totient numbers and an exposition of the results given in the paper On Perfect Totient Numbers by Douglas E. Iannuci, et al. which appeared in the Journal of Integer Sequences, Vol. 6 (2003), Article 3.4.5. For every positive integer n and n=3kp to be a perfect totient number (PTN) where s=2a3b + 1, r=2c3ds + 1, q=2e3f r+1, p=2g3hq + 1 are all primes where a,c,e,g≥1, b,d,f,h≥0 and k≤20. New classes of PTNs of the form n=33p were identified.
Keywords: Euler’s function, arithmetic function, positive integers, integer sequences, iteration, class number
Lasaliksik is a peer-reviewed journal published by the University Research Office of De La Salle University-Dasmariñas (DLSU-D) and serves as the University’s official publication for Science and Mathematics. The title of the journal highlights the Filipino word “saliksik” which translates to “to search/ research” and thus the journal’s goal of disseminating newly discovered knowledge as well as developments and extended results of scientific studies. More importantly, the journal aims to provide an academic platform for researchers to share their scholarly works and research endeavors in various disciplines of science and mathematics, both pure and applied.
Lasaliksik accepts original full articles, expository studies, research notes, review articles and perspectives for review and releases one volume per year having two issues.
Editorial Board
Editor-in-Chief
Dr. Cristina C. Salibay (Biology, De La Salle University-Dasmariñas)
Associate Editor
Dr. Ma. Theresa Christine C. Valdez (Mathematics, De La Salle University- Dasmariñas)
Members
Dr. Edwin A. Balila (Statistics, Adventist University of the Philippines)
Dr. Drexel H. Camacho (Chemistry, De La Salle University, Manila)
Dr. Rubie M. Causaren (Animal Science, De La Salle University-Dasmariñas)
Dr. Melanie M. Guiang (Plant Science, Central Mindanao University)
Dr. Janet M. Luistro (Ecotoxicology, De La Salle University-Dasmariñas)
Dr. Maria Carla F. Manzano (Physics, De La Salle University Manila)
Dr. Veeranoot Nissapatorn (Microbio and Parasitology, Walailak University Thailand)
Dr. Marie Christine M. Obusan (Environmental Science, University of the Philippines, Diliman)
Dr. Hanna Arini Parhusip (Applied Mathematics, Universitas Kristen Satya Wacana, Indonesia)
Dr. Maria de Lourdes Gomes Periera (Cell and Molecular Biology, University of Aviero, Portugal)
Dr. Elizabeth B. Villa (Criminology, De La Salle University-Dasmariñas)
Editorial Assistant
Mr. Jaime Zeus C. Agustin (Research Communication, Dissemination and Utilization Coordinator, University Research Office, De La Salle University-Dasmariñas)