Alpha Graceful Labeling in the Context of 𝑚-Shadow Graphs

J. H. Jani; V. J. Kaneria

doi:https://doi.org/10.14445/22315373/IJMTT-V72I2P101

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 2 | Year 2026 | Article Id. IJMTT-V72I2P101 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I2P101

Alpha Graceful Labeling in the Context of 𝑚-Shadow Graphs

J. H. Jani, V. J. Kaneria

Received	Revised	Accepted	Published
06 Dec 2025	14 Jan 2026	05 Feb 2026	21 Feb 2026

Citation :

J. H. Jani, V. J. Kaneria, "Alpha Graceful Labeling in the Context of 𝑚-Shadow Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 2, pp. 1-5, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I2P101

Abstract

A graph 𝐺 = (𝑉,𝐸) is said to be 𝛼-graceful if there exists one-to-one function 𝑓 from 𝑉(𝐺) to the set {0, 1,2, .. ., |𝐸(𝐺)| } such that each edge 𝑥𝑦 is assigned the label |𝑓(𝑥) − 𝑓(𝑦)|, then the resulting edge labels are distinct, and there exists an integer 𝑘 such that, 𝑚𝑖𝑛{𝑓(𝑥),𝑓(𝑦)} ≤ 𝑘 < 𝑚𝑎𝑥{𝑓(𝑥),𝑓(𝑦)} for each edge 𝑥𝑦 of 𝐺. In this paper, we derive α-graceful labeling for the 𝑚-shadow graph of various standard graphs.

Keywords

Graceful labeling, 𝜶-graceful labeling, m-shadow graph.

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