Algorithms for Zumkeller Labeling of Full Binary Trees and Square Grids

Balamurugan, B. J.; Thirusangu, K.; Thomas, D. G.

doi:10.1007/978-81-322-2135-7_21

Cited by 9 publications

(5 citation statements)

References 1 publication

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“…The mean graph labeling was introduced by Somasundaram and Ponraj in [18]. Balamurugan, Thirusangu and Thomas introduced the notion of Zumkeller labeling in [2]. Hussain and Tabraiz investigated Super d-antimagic labeling of subdivided kC 5 in [10].…”

Section: Introductionmentioning

confidence: 99%

Novel classes of integers and their applications in graph labeling

Ali

Mahmood

Shum

2021

Hacettepe Journal of Mathematics and Statistics

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Adding new classes of integers to literature is both challenging and charming. Until a new class is completely characterized, mathematics is never going to be worth it. While it's absurd to play with integers without intended consequences. In this work, we introduce and investigate four new classes of integers namely, anti-totient numbers, half anti-totient numbers, near Zumkeller numbers and half near Zumkeller numbers by using the notion of non-coprime residues of n including n. We formulate and propose relations of these new classes of numbers with previous well-known numbers such as perfect, totient, triangular, pentagonal, and hexagonal numbers. These new classes of integers have been completely characterized. Finally, as an application of these new classes of numbers, a new graph labeling is also proposed on anti-totient numbers.

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Section: Introductionmentioning

confidence: 99%

Novel classes of integers and their applications in graph labeling

Ali

Mahmood

Shum

2021

Hacettepe Journal of Mathematics and Statistics

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“…introduced the concept of Zumkeller labeling in in the year 2013 [2]. The idea of Zumkeller labeling of some simple graphs has been previously reported [3,4,5,6,11].…”

Section: Introductionmentioning

confidence: 99%

Zumkeller labeling of some path related graphs

Wilson¹,

Bebincy²

2021

Malaya J. Mat.

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A positive integer n is said to be Zumkeller number if its positive factors can be partitioned into 2 disjoint parts with the equal sum, that is each part with sum σ (n)/2. Let G = (V (G), E(G)) be a graph. An one to one function f defined on V (G) to a subset of natural numbers is termed as Zumkeller labeling of G if the induced function) admits Zumkeller labeling is called a Zumkeller graph. In this manuscript, we investigate Zumkeller labeling for several classes of path graph.

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“…The Zumkeller graphs were introduced by Balamurugan et al in [3] in the year 2014. Also in the literature [1][2][3][4][5][6],the Zumkeller graphs, Strongly multiplicative Zumkeller graphs and k-Zumkeller graphs have been introduced and investigated by Balamurugan et al In this paper, we investigate the existence of Zumkeller complete graphs and Zumkeller fan graphs.…”

Section: Introductionmentioning

confidence: 99%

Zumkeller Labeling of Complete Graphs

Balamurugan¹,

Meenakshi²

2019

IJEAT

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Let G (V, E) be a graph with vertex set V and edge set E. The process of assigning natural numbers to the vertices of G such that the product of the numbers of adjacent vertices of G is a Zumkeller number on the edges of G is known as Zumkeller labeling of G. This can be achieved by defining an appropriate vertex function of G. In this article, we show the existence of this labeling to complete graph and fan graph.

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Algorithms for Zumkeller Labeling of Full Binary Trees and Square Grids

Cited by 9 publications

References 1 publication

Novel classes of integers and their applications in graph labeling

Novel classes of integers and their applications in graph labeling

Zumkeller labeling of some path related graphs

Zumkeller Labeling of Complete Graphs

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