On e-super (a, d)-edge antimagic total labeling of total graphs of paths and cycles

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Saibulla A.; Pushpam P. Roushini Leely

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Journal Paper

Paper Information

Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2025 | Volume:10 | Issue:4 Page(s): 787-802

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Title

On e-super (a, d)-edge antimagic total labeling of total graphs of paths and cycles

Author(s)

Saibulla A. | Pushpam P. Roushini Leely | Issue Writer Certificate

Keywords

graph labeling

magic labeling

antimagic labeling

Abstract

A (p, q)-graph G is (a, d)-edge antimagic total if there exists a bijection f from V (G) ∪ E(G) to {1, 2, . . ., p + q} such that for each edge uv ∈ E(G), the edge weight Λ(uv) = f(u) + f(uv) + f(v) forms an arithmetic progression with first term a > 0 and common difference d ≥ 0. An (a, d)-edge antimagic total labeling in which the vertex labels are 1, 2, . . ., p and edge labels are p + 1, p + 2, . . ., p + q is called a super (a, d)-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, . . ., q and vertex labels are q + 1, q + 2, . . ., 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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