Super (a,d)-H-antimagic labeling of subdivided graphs

Taimur, Amir; Numan, Muhammad; Ali, Gohar; Mumtaz, Adeela; Semaničová-Feňovčíková, Andrea

doi:10.1515/math-2018-0062

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…If the vertices of 𝐺 are labeled with 1,2, … , |𝑉(𝐺)|, then 𝑓 is called the super (𝑎, 𝑑)-𝐻-antimagic total labeling of 𝐺 and 𝐺 is called the super (𝑎, 𝑑)-𝐻-antimagic. The readers are referred to (Martin Bača et al, 2006;Agustin et al, 2019;Hussain et al, 2012.;Inayah et al, 2013;Palanivelu & Neela, 2019;Permata Sari et al, 2019;Prihandini & Adawiyah, 2023;Raheem et al, 2014;Taimur et al, 2018) for other results about super (𝑎, 𝑑)-𝐻-antimagic.…”

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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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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“…A super (a,d)-Bm-antimagic total covering of a generalized amalgamation of Fan Graphs was discovered by (Agustin et al, 2017) An antimagic total labeling on Double Cones was investigated (Roswitha et al, 2019). Super antimagic labeling of subdivided graph was discovered by (Taimur et al, 2018). Super sub division of cycle also has super antimagic total labeling (Bhatavadekar, 2021).…”

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confidence: 99%

On Super (a,d)-C_3- Antimagic Total Labeling of Dutch Windmill Graph D_3^m

Irene,

Mahmudi,

Nurmaleni

2024

Mathline

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This paper is aimed to investigate the existence of super (a,d)-C_3- antimagic total labeling of dutch windmill graph D_3^m . The methods to achieves the goal was taken in three step. First of all determine the edge and vertices notation on dutch windmill graph . At the second step, labeling the vertices and edges of several dutch windmill graphs, then obtained the pattern. Finally pattern must be proven to become theorem. Based on the study, The Dutch Windmill Graph D_3^m, with m>=2 has super (14m+9,5)-C_3- antimagic total labeling, super (13m+8,3)-C_3- antimagic total labeling, super (12m+9.,5)-C_3- antimagic total labeling, super (11m+10.,7)-C_3- antimagic total labeling, super (10m+8.,3)-C_3- antimagic total labeling.

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Super (a,d)-H-antimagic labeling of subdivided graphs

Abstract: A simple graph G = (V , E) admits an H-covering, if every edge in E(

Cited by 2 publications

References 9 publications

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

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

On Super (a,d)-C_3- Antimagic Total Labeling of Dutch Windmill Graph D_3^m

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