Abstract
Let G = (V, E) be a graph. An injective function f: V → N is said to be a Zumkeller labeling of the graph G, if the induced function f *: E → N defined as f *(xy) = f(x) f(y) is a Zumkeller number for all xy ∈ E, x, y ∈ V. A graph G = (V, E) which admits a Zumkeller labeling is called a Zumkeller graph. In this paper, we provide algorithms for Zumkeller labeling of full binary trees and grid graphs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
B.J. Balamurugan, K. Thirusangu, D.G. Thomas, Strongly multiplicative Zumkeller labeling of graphs. Int. Conf. Inf. Math. Sci. 349–354 (2013)
G.S. Bloom, S.W. Golomb, Applications of numbered undirected graphs. IEEE 165(4), 526–570 (1977)
F. Buss, Zumkeller numbers and partitions. http://groups.google.de/group/de.sci.mathematik/msg/e3fc5afcec2ae540
J.A. Gallian, A dynamic survey of graph labeling. Electron. J. Comb. 16 (2013)
F. Harary, Graph theory (Addison-Wesley, Reading Mass, 1972)
R. Johnsonbaugh, Discrete mathematics (Pearson Education, Asia, 2001)
Y. Peng, K.P.S. Bhaskara Rao, On zumkeller numbers. J. Number Theory 133(4), 1135–1155 (2013)
A. Rosa, On certain valuations of the vertices of a graph, in Theory of Graphs. International Symposium (1966), pp. 349–359
A.K. Srinivasan, Practical numbers. Curr. Sci. 17, 179–180 (1948)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer India
About this paper
Cite this paper
Balamurugan, B.J., Thirusangu, K., Thomas, D.G. (2015). Algorithms for Zumkeller Labeling of Full Binary Trees and Square Grids. In: Suresh, L., Dash, S., Panigrahi, B. (eds) Artificial Intelligence and Evolutionary Algorithms in Engineering Systems. Advances in Intelligent Systems and Computing, vol 325. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2135-7_21
Download citation
DOI: https://doi.org/10.1007/978-81-322-2135-7_21
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2134-0
Online ISBN: 978-81-322-2135-7
eBook Packages: EngineeringEngineering (R0)