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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika)
Yatin, Bela Zainun
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Mathematics

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Super (a,d)-P_2⨀P_m-Antimagic Total Labeling of Corona Product of Two Paths Yatin, Bela Zainun; Awanis, Zata Yumni; Wardhana, I Gede Adhitya Wisnu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20065

Abstract

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.
Co-Authors I Gede Adhitya Wisnu Wardhana Zata Yumni Awanis