Mathematics and Computational Sciences

Locally harmonious coloring of variants of hypercubes

Document Type : Original Article

Authors

Lenin Muthu Kumaran 1
Sivaa Manokaran 1
Arul Amirtha Raja 2
Santiagu Theresal 3

1 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Vellore, Tiruvannamalai-606 603, Tamil Nadu, India.

2 Department of Mathematics, St.Joseph's College of Engineering, OMR,Chennai 600119, India.

3 Department of Mathematics, Auxilium College of Arts and Science for Women, Regunathapuram, Affiliated to Bharathidasan University,Tiruchirappalli.

https://doi.org/10.30511/mcs.2025.2076210.1583
Abstract
This paper investigates the concept of locally harmonious coloring in the context of high-dimensional interconnection net works, specifically the hypercube Qn, its structural variants such as the folded hypercube FQn, the augmented cube AQn, and the crossed cube CQn. We aim to determine χlh(Qn), χlh(FQn), χlh(AQn), and χlh(CQn), and to analyze how dimensional variations and structural augmentations influence their locally harmonious colorability. Furthermore, we establish relationships
between χlh and other graph invariants such as degree, diameter, and automorphism group symmetry. The study provides new insights into the combinatorial structure of hypercube-based networks and their applications in parallel architectures, fault tolerant communication, and distributed computation.

Keywords

Locally Harmonious Coloring
Hypercube Qn
Folded Hypercube FQn

Subjects

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Mathematics and Computational Sciences
Volume 7, Issue 1
Winter 2026
Pages 138-151

  • Receive Date 30 October 2025
  • Revise Date 13 December 2025
  • Accept Date 23 December 2025

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