Alpha Graceful Labeling in the Context of π‘š-Shadow Graphs

International Journal of Mathematics Trends and Technology 2026 Open access

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Authors: Jani J. H., V. J. Kaneria
DOI: 10.14445/22315373/ijmtt-v72i2p101
Cited by: 0

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 π‘₯𝑦 is assigned the label |𝑓(π‘₯) βˆ’ 𝑓(𝑦)|, then the resulting edge labels are distinct, and there exists an integer π‘˜ such that, π‘šπ‘–π‘›{𝑓(π‘₯),𝑓(𝑦)} ≀ π‘˜ < π‘šπ‘Žπ‘₯{𝑓(π‘₯),𝑓(𝑦)} for each edge π‘₯𝑦 of 𝐺. In this paper, we derive Ξ±-graceful labeling for the π‘š-shadow graph of various standard graphs.

Fields of Study & Subjects

Graph Labeling and Dimension Problems Advanced Graph Theory Research Smarandache Functions and Recreational Number Theory

Publication details

Journal / source
International Journal of Mathematics Trends and Technology
Volume
72
Issue
2
Pages
1–5
Publication date
25 February 2026
Language
EN