Modular Irregular Labeling on Double-Star and Friendship Graphs

Sugeng, Kiki Ariyanti; Barack, Z. Z.; Hinding, Nurdin; Simanjuntak, Rinovia

doi:10.1155/2021/4746609

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…The modular irregularity strength for some graphs have known, such as path, star, tree, cycle, gear graph [4] , fan graph [3] , and wheel graph [1] . Recently, Sugeng, et al have determined the modular irregularity strength of double stars and friendship graphs [12] .…”

Section: Modular Irregular Labelling On Dodecahedral Modified General...mentioning

confidence: 99%

Two types irregular labelling on dodecahedral modified generalization graph

Hinding

Sugeng

Nurlindah

et al. 2022

Heliyon

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Section: Modular Irregular Labelling On Dodecahedral Modified General...mentioning

confidence: 99%

Two types irregular labelling on dodecahedral modified generalization graph

Hinding

Sugeng

Nurlindah

et al. 2022

Heliyon

Self Cite

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“…Bača et al also determined the modular irregularity strength of the fan graph [5] and wheel [6]. Then Sugeng et al determined the modular irregularity strength of double-star and friendship graphs [7]. Tilukay determined the modular irregularity strength of the triangular book graph [8].…”

Section: Introductionmentioning

confidence: 99%

Modular irregularity strength of disjoint union of cycle-related graph

Barack,

Sugeng

2024

ITM Web Conf.

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Let G = (V,E) be a graph with a vertex set V and an edge set E of G, with order n. Modular irregular labeling of a graph G is an edge k-labeling φ:E → {1, 2,…,k} such that the modular weight of all vertices is all different. The modular weight is defined by wtφ(u) = Σv∈N(u) φ(uv) (mod n). The minimum number k such that a graph G has modular irregular labeling with the largest label k is called modular irregularity strength of G. In this research, we determine the modular irregularity strength for a disjoint union of cycle graph, $ (mC_{n})=\frac{mn}{2}+1 $ for n ≡ 0 (mod 4), a disjoint union of sun graph, ms(m(Cn ⊙ K1))2 = ∞ for n and m even and ms(m(Cn ⊙ K1)) = mn otherwise, and a disjoint union of middle graph of cycle graph, ms(mM(Cn)) = ∞ for n and m both odd numbers and $(mM({C_n})) = {{mn} \over 2} + 1$ otherwise.

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“…In the same year, Bača et al in [3] found the modular irregularity strength of wheels W n . Sugeng et al in [14] provided the results for the modular irregularity strength of double-stars S k,k and friendship graphs f n .…”

Section: Introductionmentioning

confidence: 99%

Modular irregularity strength on some flower graphs

Sugeng¹,

John²,

Lawrence³

et al. 2023

EJGTA

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Let G = (V (G), E(G)) be a graph with the nonempty vertex set V (G) and the edge set E(G). Let Z n be the group of integers modulo n and let k be a positive integer. A modular irregular labeling of a graph G of order n is an edge k-labeling φ : E(G) → {1, 2, . . . , k}, such that the induced weight function σ : V (G) → Z n defined by σ(v) = u∈N (v) φ(uv) (mod n) for every vertex v ∈ V (G) is bijective. The minimum number k such that a graph G has a modular irregular k-labeling is called the modular irregularity strength of a graph G, denoted by ms(G). In this paper, we determine the exact values of the modular irregularity strength of some families of flower graphs, namely rose graphs, daisy graphs and sunflower graphs.

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Modular Irregular Labeling on Double-Star and Friendship Graphs

Abstract: A modular irregular graph is a graph that admits a modular irregular labeling. A modular irregular labeling of a graph G of order n is a mapping of the set of edges of the graph to 1,2 , … Show more

Cited by 10 publications

References 7 publications

Two types irregular labelling on dodecahedral modified generalization graph

Two types irregular labelling on dodecahedral modified generalization graph

Modular irregularity strength of disjoint union of cycle-related graph

Modular irregularity strength on some flower graphs

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