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Abstract

The attractive properties of the hypercube graph such as its diameter, good connectivity, and symmetry have made it a popular topology for the design of multi-computer interconnection networks. Efforts to improve some of these properties have led to the evolution of hypercube variants. Let c be the proper coloring of graph G, where the neighboring vertices will get individual colors. Coloring c is irregular if distinct vertices have distinct color codes and the least number of colors that ought to receive an irregular coloring is the irregular chromatic number, χ_ir (G). In this paper, we discuss the irregular coloring and find the irregular chromatic number for the hypercube graph Q_n and some of its variants using binomial coefficients for the Locally twisted cube graph LTQ_n, Crossed cube graph CQ_n and two types of Fractal cubic network graph FCNG₁ (k) and FCNG₂ (k).

Keywords

Irregular coloring irregular chromatic number hypercube graph variants of hypercube graph

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Irregular chromatic number for hypercube graph and its variants

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