Near-Zumkeller numbers

Patodia, Harish; Saikia, Helen K.

doi:10.22199/issn.0717-6279-4320

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2023

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“…Generalizing the concept of Zumkeller number H. Patodia and H. K. Saikia defined a new type of number as m-Zumkeller number in [5].…”

Section: Introductionmentioning

confidence: 99%

A note on m-Zumkeller cordial labeling of graphs

Patodia

Saikia

2023

Proyecciones (Antofagasta)

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Let G = (V,E) be a graph. An m-Zumkeller cordial labeling of the graph G is defined by an injective function f : V → N such that there exists an induced function f ∗ : E → {0, 1} defined by f ∗ (uv) = f (u) · f (v) that satisfies the following conditions- i. For every uv ∈ E, f ∗ (uv) = {█(1,if f (u) · f (v) is an m-Zumkeller number @ 0,otherwise )┤ ii. |ef ∗ (0) − ef∗ (1)| ≤ 1 where ef ∗ (0) and ef ∗ (1) denote the number of edges of the graph G having label 0 and 1 respectively under f ∗. In this paper we prove that there exist an m-Zumkeller cordial labeling of graphs in paths, cycles, comb graphs, ladder graphs, twig graphs, helm graphs, wheel graphs, crown graphs and star graphs.

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“…Generalizing the concept of Zumkeller number H. Patodia and H. K. Saikia defined a new type of number as m-Zumkeller number in [5].…”

Section: Introductionmentioning

confidence: 99%