Decomposition of hypercubes into sunlet graphs

2021/07/21 by A. V. Sonawane, Sonawane, A. V. · 1 citation
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Interconnection Networks and Systems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2107.10313

openalex publication_date 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any positive integer k ≥ 3, the sunlet graph of order 2k, denoted by L_2k, is the graph obtained by adding a pendant edge to each vertex of a cycle of length k. In this paper, we prove that the necessary and sufficient condition for the existence of an L₁₆-decomposition of the n-dimensional hypercube Q_n is n = 4 or n ≥ 6. Also, we prove that for any integer m ≥ 2, Q_mn has an L_2k-decomposition if Q_n has a C_k-decomposition.

Cited by

• Sunlet factors for Cartesian products of cycles

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