Abstract
For any integer $k\geq 3$ , we define sunlet graph of order $2k$, denoted by $L_{2k}$, as the graph consisting of a cycle of length $k$ together with $k$ pendant vertices, each adjacent to exactly one vertex of the cycle. In this paper, we give necessary and sufficient conditions for the existence of $L_{8}$-decomposition of tensor product and wreath product of complete graphs.
Highlights
All graphs considered here are finite, simple and undirected
For any integer k ≥ 3, we define sunlet graph of order 2k, denoted by L2k, as the graph consisting of a cycle of length k together with k pendant vertices, each adjacent to exactly one vertex of the cycle
A cycle of length k is called k-cycle and it is denoted by Ck
Summary
All graphs considered here are finite, simple and undirected. For the standard graph-theoretic terminology the readers are referred to [7]. We give necessary and sufficient conditions for the existence of L8-decomposition of tensor product and wreath product of complete graphs. Akwu and Ajayi [1] obtained the necessary and sufficient conditions for the existence of decomposition of Kn ⊗ Km and (Kn − I) ⊗ Km, where I denote the 1-factor of a complete graph into sunlet graph of order twice the prime.
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