Odd-Even Sum Labeling of some Graphs

Monika, K.; Murugan, K.

doi:10.26708/ijmsc.2017.1.7.07

Cited by 2 publications

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“…Grap is said to be an odd-even sum graph if there exists an injective function ∶ → {±1, ±2, ±3, … , ±(2 − 1)} such that induced a bijection * : → {2, 4, 6, … , 2 } with * ( ) = ( ) + ( ), ∀ ∈ . The function is called an odd-even sum labeling of [1].…”

Section: Introductionmentioning

confidence: 99%

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An Odd-Even Sum Labeling of Jellyfish and Mushroom Graphs

Nurhakim

2020

InPrime:Ind.Jour.Pure.Applied.Math

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A graph G(V,E) with p vertices and q edges called graph odd-even sum if there exists an injective function f from V to {+ 1, +2, +3, ..., +(2p-1)} such that induced a bijection f*(uv)=f(u)+f(v) as label of edge and u,v element of V forms the set {2,4,...,2q}, and f is called odd-even sum labeling. There are three criteria of graphs that can be labeled by this labeling, they are undirected, no loops, and finite for every edges and vertex. Jellyfish J(m,n) graph and Mushroom Mr(m) graph have the criteria. So in this paper will be showed that the Jellyfish and Mushroom graphs can be labeled by this labeling.Keywords: odd-even sum graph; odd-even sum labeling; Jellyfish and mushroom graphs. AbstrakGraf G(V,E) dengan banyak titik p dan sisi q dikatakan graf jumlah ganjil-genap jika terdapat suatu fungsi injetif f dari V ke {+ 1, +2, +3, ..., +(2p-1)} sehingga bijektif f*(uv)=f(u)+f(v) merupakan label sisi dengan u,v anggota dari V membentuk himpunan bilangan {2,4,...,2q}, dengan f merupakan pelabelan jumlah ganjil-genap. Kriteria graf yang dapat dilabeli oleh pelabelan jumlah ganjil-genap ada tiga, yaitu graf yang tidak berarah, tidak memiliki loop, dan terhingga, baik secara sisi maupun titik. Graf Jellyfish J(m,n) dan Mushroom Mr(m) memenuhi ketiga kriteria tersebut. Pada tulisan ini akan ditunjukkan bahwa kedua graf tersebut dapat dilabeli dengan pelabelan jumlah ganjil-genap.Keywords: graf jumlah ganjil-genap; pelabelan jumlah ganjil-genap; graf Jellyfish dan graf Mushroom.

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Section: Introductionmentioning

confidence: 99%

“…Arockiaraj et al [5] introduced the odd-sum labeling of sum subdivision graphs. Monika and Murugan [1] proved that a path , ≥ 2, a star , , and caterpillar graph are odd-even sum labeling. In this paper, we proved that a Jellyfish and Mushroom graphs are odd-even sum graphs.…”

Section: Introductionmentioning

confidence: 99%