On e-Super (a, d)-Edge Antimagic Total Labeling of Total Graphs of Paths and Cycles

Document Type : Original paper

Authors

1 Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology.

2 Department of Mathematic, D.B. Jain College, Chennai - 600097, Tamil Nadu, India

Abstract

A $(p, q)$-graph $G$ is  {\it $(a, d)$-edge antimagic total} if there exists a bijection $f$ from $V(G) \cup E(G)$ to $\{1, 2, \dots, p+q\}$ such that for each edge $uv \in E(G)$, the edge weight $\Lambda(uv) = f(u) + f(uv) + f(v)$ forms an arithmetic progression with first term $a > 0$ and common difference $d \geq 0$. An $(a, d)$-edge antimagic total labeling in which the vertex labels are $1, 2, \dots, p$ and edge labels are $p+1, p+2, \dots, p+q$ is called a {\it super} $(a, d)$-{\it edge antimagic total labeling}. Another variant of $(a, d)$-edge antimagic total labeling called as e-super $(a, d)$-edge antimagic total labeling in which the edge labels are $1, 2, \dots, q$ and vertex labels are $q+1, q+2, \dots, q+p$. In this paper, we investigate the  existence of e-super $(a, d)$-edge antimagic total labeling for total graphs of paths, copies of cycles and disjoint union of cycles.

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References

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Available Online from 10 February 2024

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