Advances and Applications in Discrete Mathematics
Volume 27, Issue 1, Pages 1 - 14
(May 2021) http://dx.doi.org/10.17654/DM027010001 |
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t-m-ZUMKELLER LABELING OF GRAPHS
Harish Patodia and Helen K. Saikia
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Abstract: A positive integer n is called an m-Zumkeller number if the set of all the positive divisors of n can be partitioned into two disjoint subsets of equal product. Let be a graph. A one-one function is called a t-m-Zumkeller labeling of the graph G if the induced function defined by satisfies the following conditions:
- For every is an m-Zumkeller number.
- where t denotes the number of distinct m-Zumkeller numbers on the edges of G.
If a graph admits a t-m-Zumkeller labeling, then the graph is known as t-m-Zumkeller graph. In this paper, we prove the existence of t-m-Zumkeller labeling of different types of graphs viz., (i) paths, (ii) cycles, (iii) comb graphs, (iv) ladder graphs and (v) twig graphs. |
Keywords and phrases: m-Zumkeller numbers, t-m-Zumkeller labeling, comb graphs, ladder graphs, twig graphs.
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