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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 : Electronic Journal of Graph Theory and Applications (EJGTA)

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A note on Fibonacci and Lucas number of domination in path Leomarich F Casinillo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.11

Abstract

Let G = (V(G), E(G)) be a path of order n ≥ 1. Let fm(G) be a path with m ≥ 0 independent dominating vertices which follows a Fibonacci string of binary numbers where 1 is the dominating vertex. A set F(G) contains all possible fm(G), m ≥ 0, having the cardinality of the Fibonacci number Fn + 2. Let Fd(G) be a set of fm(G) where m = i(G) and Fdmax(G) be a set of paths with maximum independent dominating vertices. Let lm(G) be a path with m ≥ 0 independent dominating vertices which follows a Lucas string of binary numbers where 1 is the dominating vertex. A set L(G) contains all possible lm(G), m ≥ 0, having the cardinality of the Lucas number Ln. Let Ld(G) be a set of lm(G) where m = i(G) and Ldmax(G) be a set of paths with maximum independent dominating vertices. This paper determines the number of possible elements in the sets Fd(G), Ld(G), Fdmax(G) and Ldmax(G) by constructing a combinatorial formula. Furthermore, we examine some properties of F(G) and L(G) and give some important results.
Co-Authors Divina L Valenzona Emily L Casinillo Ginna F Tavera Jorge S Valenzona Leizl F Abrantes Leo A Mamolo Michael G Suarez