NILAI KETAKTERATURAN SISI TOTAL PADA GRAF AMALGAMASI SUBDIVISI GRAF DOVETAIL

Eka Nurdini; Isnaini Rosyida; Mulyono Mulyono

doi:10.15294/ujm.v9i1.28719

Arockiamary, S. T. (2016). Total edge irregularity strength of diamond snake and dove. IJPAM(109), 125-132.
Baca, M., Jendrol, S., Miller, M., & Ryan, J. (2007). On Irregular Total Labellings. Discrete Mathematics 307, 1378-1388.
Bondy, J. A., & Murty, U. S. (1976). Graph Theory with Applications. Ontario: Departement of Combinatorics and Optimization, University of Waterloo.
Budayasa, I. K. (2007). Teori Graf dan Aplikasinya. Surabaya: Unesa University Press.
Chartrand, G. (1986). Introductory Graph Theory. New York: Dover Publications Inc.
Chartrand, G., & Lesniak, L. (1996). Graph and Digraph Third Edition. Florida: Chapman and Hall/CRC.
Chartrand, G., & Oellermann, O. R. (1993). Applied and Algorithmic Graph Theory. New York: McGraw-Hill Inc.
Gallian, J. A. (2011). A Dynamic Survey of Graph Labeling. Minnesota: Department of Mathematics and Statistics, University of Minnesota Duluth.
Harary, F. (1994). Graph Theory. Michigan: Addison-Wesley Publishing Company.
Indriati, D., dodo, W., jayanti, I. E., Sugeng, K. A., & BaË‡ca, M. (2015). On To tal Edge Irregularity Strength o f Generalized Web Graphs and Related Graphs. Mathematics in Computer Science.
IvanÄo, J., & JendroË‡l, S. (2006). Total edge irregularity strength of trees. Discussiones Math. Graph Theory(26), 449-456.
Johnsonbaugh, R. (2001). Discrete Mathematics. Fifth edition. New Jersey: Prentice Hall.
Khan, I. F., Poshni, M. I., & Gross, J. L. (2010). Genus distribution of graph amalgamations: Pasting when one root has arbitrary degree. ARS MATHEMATICA CONTEMPORANEA 3, 121-138.
Marzuki, C. C., Salman, A. N., & Miller, M. (2013). On The Total Irregularity Strength of Cycles and Paths. Far East J. Math. Sci., 1-21.
Nurdin, Baskoro, E. T., M, A. N., & Gaos, N. N. (2010). On the total vertex irregularity strength of trees. Discrete Math 310, 3043-3048.
Rosen, K. H. (2013). Global Edition Discrete Mathematics and Its Applications Seventh Edition. New York: McGraw-Hill.
Rosyida, I., Widodo, & Indriati, D. (2018). On total irregularity strength of caterpillar graphs with two leaves on each internal vertex. J of Phys: Conference Series 1008(1), 12046.
Vasudev, C. (2006). Graph Theory with Applications. New Delhi: New age international publisher.
Wallis, W. D. (2001). Magic Graph. Boston: Birkhauser.

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Affiliations

Eka Nurdini
Universitas Negeri Semarang

Isnaini Rosyida
Universitas Negeri Semarang

Mulyono Mulyono
Universitas Negeri Semarang

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NILAI KETAKTERATURAN SISI TOTAL PADA GRAF AMALGAMASI SUBDIVISI GRAF DOVETAIL

Eka Nurdini ,
Isnaini Rosyida ,
Mulyono Mulyono

Vol 9 No 1 (2020)

DOI 10.15294/ujm.v9i1.28719

Submitted: Feb 1, 2019

Published: Jun 22, 2020

Abstract

Given a graph G(V,E) with a non-empty set V of vertices and a set E of edges. A total labelling Î»:VâˆªEâ†’{1,2,â€¦,k} is called an edge irregular total labelling if the weight of every edge is distinct. The weight of an edge e, under the total labelling Î», is the sum of label of edge e and all labels of vertices that are incident to e. In other words, w(xy)=Î»(xy)+Î»(x)+Î»(y). The total edge irregularity strength of G, denoted by tes(G) is the minimum k used to label graph G with the edge irregular total labelling. In this paper, authors investigate the total edge irregularity strength of Amalgamation between Subdivision of Dovetail graph with pendant vertices and cycle graph (ã€–SDã€—_n^n,x)*(C_(3n-3),z). The results of this research are tes((ã€–SDã€—_n^n,x)*(C_(3n-3),z))=âŒˆ(9n-3)/3âŒ‰.