A Conjecture on Super Edge-Magic Total Labeling of 4-Cycle Books

Simanihuruk, Mudin; Kusmayadi, Tri Atmojo; Baki, Swita; Romala, Minsi; Damanik, Friska

doi:10.1155/2021/8483926

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…Furthermore, Llado A & Moragas J (2007) and Ngurah et al (2010) investigated cyclesupermagic total labellings for certain connected graphs. The readers are referred (Anjaneyulu et al, 2015;Sandariria et al, 2017;Simanihuruk et al, 2021;Lakshmi & Sagayakavitha, 2018;Ulfatimah et al, 2017;Agustin et al, 2019;Murugan & Chandra Kumar, 2019) for other results about 𝐻-(super) magic total labelling.…”

Section: A Introductionmentioning

confidence: 99%

Super (a,d)-P_2⨀P_m-Antimagic Total Labeling of Corona Product of Two Paths

Yatin,

Awanis,

Wardhana

2024

JTAM

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Graph labeling involves mapping the elements of a graph (edges and vertices) to a set of positive integers. The concept of an anti-magic super outer labeling (a,d)-H pertains to assigning labels to the vertices and edges of a graph using natural numbers {1,2,3,...,p+q}. The weights of the outer labels H form an arithmetic sequence {a,a+d,a+2d,...,a+(k-1)d}, where 'a' represents the first term, 'd' is the common difference, and 'k' denotes the total number of outer labels, with the smallest label assigned to a vertex. This study investigates the super (a,d)-P_2⨀P_m-antimagic total labeling of the corona product P_n⨀P_m, where n and m are both greater than or equal to 3. We define the labeling functions for vertices and edges based on the partitioning of labels into three subsets. Using k-balanced and (k,δ)-anti balanced multisets, we demonstrate that for m being odd, P_n⨀P_m is super (9m^2 n+4mn+m-n+3,1)-P_2 ⨀▒P_(m ) -antimagic, and for m being even, P_n⨀P_m is super (9m^2 n+4mn+m-2n+5,3)-P_2 ⨀▒P_(m ) -antimagic. The labeling scheme is illustrated through examples. For the case when m is odd, an antimagic total labeling of P_3 ⨀▒P_3 forms a super (282,1)- P_2 ⨀▒P_(3 ) -antimagic labeling. In the case of even m, an antimagic total labeling of P_3 ⨀▒P_(4 ) results in a super (483,3)- P_2 ⨀▒P_(4 ) -antimagic labeling. Both of these examples provide insights into the antimagic properties of corona products.

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