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All Journal Jurnal Pendidikan Indonesia Electronic Journal of Graph Theory and Applications (EJGTA) Indonesian Journal of Mathematics Education The Indonesian Journal of Social Studies InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Fundamental Mathematics and Applications (JFMA) Indonesian Journal Of Educational Research and Review
Leomarich F Casinillo
Visayas State University
Humanities Computer Science & IT Decision Sciences, Operations Research & Management Education Electrical & Electronics Engineering Mathematics Social Sciences Other

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Journal : InPrime: Indonesian Journal Of Pure And Applied Mathematics

 1 
Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs Leomarich F Casinillo; Leo A Mamolo
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v2i2.15845

Abstract

AbstractThis paper developed a simple but elegant formula for the series of consecutive square of natural numbers under alternating signs. Furthermore, this study investigated the said formula under odd and even number of terms and discuss some important results.Keywords: consecutive -squares; alternating signs; odd and even terms. AbstrakDalam paper ini kita membangun formula yang sederhana namun elegan untuk menghitung jumlah deret berganti-tanda dari kuadrat bilangan-bilangan asli berurutan.  Kita akan menyelidiki formula untuk kasus banyaknya suku ganjil maupun genap dan mendiskusikan beberapa hasil yang penting.Kata kunci: -kuadrat berurutan; berganti-tanda; bersuku ganjil dan bersuku genap.
On Triangular Secure Domination Number Emily L Casinillo; Leomarich F Casinillo; Jorge S Valenzona; Divina L Valenzona
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v2i2.15996

Abstract

Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m  if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m).  A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m)  is called a secure domination number of graph T_m. A secure dominating number  γ_s(T_m) of graph T_m is a triangular secure domination number if γ_s(T_m) is a triangular number. In this paper, a combinatorial formula for triangular secure domination number of graph T_m was constructed. Furthermore, the said number was evaluated in relation to perfect numbers.
Co-Authors Divina L Valenzona Emily L Casinillo Ginna F Tavera Jorge S Valenzona Leizl F Abrantes Leo A Mamolo Michael G Suarez