Karakteristik Graf Dengan Sisi Bilangan Fibonacci
DOI:
https://doi.org/10.31316/j.derivat.v11i3.6397Abstract
Let be a finite subset of Fibonacci numbers set. In this research, we construct a graph where the set of vertices contains integer numbers such that for every , there exist some edge in that satisfies the condition . By applying some properties of the Fibonacci numbers, we prove that if contains the first consecutive Fibonacci numbers then has the smallest order . Furthermore, we give the sufficient conditions for become simple graph and contains no cycle.
Keywords: edge of graph, Fibonacci number, order of graph, simple graph, cycle.
References
Alameddine, A.F. (1998). Bounds on the Fibonacci number of a maximal outerplanar graph, Fibonacci Quart. 36 (3), 206–210.
Bondy, J., & Murty, A. 2008, Graph Theory. New York: Springer.
Calkin, N.J. & Wilf, H.S. (1998). The number of independent sets in a grid graph, SIAM J. Discrete Math. 11 (1) 54–60 (electronic).
Chartrand, G., Lesniak, L., & Zhang, P. (2016). Graphs and Digraphs Sixth Edition. New York: CRC Pres.
Dosal-Trujillo, L.A., & Galeana-Sanchez, H. (2019). “On the Fibonacci numbers of the composition of graphs”, dalam Discrete Applied Mathematics. 266, 213-218.
Dutton, R., Chandrasekharan, N., & Brigham, R. (1993). On the number of independent sets of nodes in a tree, Fibonacci Quart. 31 (2), 98–104.
Engel, K. (1990). On the Fibonacci number of an m×n lattice, Fibonacci Quart. 28 (1), 72–78.
Foulds, L.R. (2011). Graph Theory Applications. New York: Springer Universitext.
Gunes, A.Y., Delen, S., Demirci, M., Cevik, A.S., & Cangul, I.N. (2020). “Fibonacci Graphs”, dalam Symmetry. 12, 1383-1395.
Hopkins, G. & Staton, W. (1984). Some identities arising from the Fibonacci numbers of certain graphs, Fibonacci Quart. 22 (3), 255–258.
Kirschenhofer, P., Prodinger, H. & Tichy, R.F. (1983). Fibonacci numbers of graphs. II, Fibonacci Quart. 21 (3). 219–229.
Kirschenhofer, P., Prodinger, H. & Tichy, R.F. (1984). Fibonacci numbers of graphs. III Planted plane trees, Fibonacci Numbers and their Applications, Patras, Mathematics Applications, vol. 28, Reidel, Dordrecht, 1986, pp. 105–120.
Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. New York: John Wiley and Sons.
Knopfmacher, A., Tichy, R.F., Wagner, S. & Ziegler, V. (2007). “Graph, partitions and Fibonacci numbers”, dalam Discrete Applied Mathematics. 155, 1175-1187.
Li, X., Li, Z., & Wang, L. (2003). The inverse problems for some topological indices in combinatorial chemistry, J. Comput. Biol. 10 (1), 47–55.
Linek, V. (1989). Bipartite graphs can have any number of independent sets, Discrete Math. 76 (2), 131–136.
Liu, J. (1994). Constraints on the number of maximal independent sets in graphs, J. Graph Theory 18 (2) 195–204.
Merrifield, R.E. & Simmons, H.E. 1989. Topological Methods in Chemistry, Wiley, New York.
Ordentlich, E. & Roth, R.M. (2004). Independent sets in regular hypergraphs and multidimensional runlength-limited constraints, SIAM J. Discrete Math. 17 (4), 615–623 (electronic).
Sagan, B.E. (1988). A note on independent sets in trees, SIAM J. Discrete Math. 1 (1), 105–108.
Sapozhenko, A.A. (2001). Independent sets and sum-free sets, Discrete Mathematics and Applications, Bansko, 2002, Research in the Mathematics and Computational Sciences, vol. 6, South-West University, Blagoevgrad, pp. 35–42.
Prodinger, H. & Tichy, R.F. (1982). Fibonacci numbers of graphs, Fibonacci Quart. 20 (1), 16–21.
Wilf, H.S. (1986). The number of maximal independent sets in a tree, SIAM J. Algebraic Discrete Methods 7 (1) 125–130.
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