Decomposing certain equipartite graphs into sunlet graphs of length 2p

For any integer r >= 3, we define the sunlet graph of order 2r, denoted L-2r, as the graph consisting of a cycle of length r together with r pendant vertices, each adjacent to exactly one vertex of the cycle. In this paper, we give necessary and sufficient conditions for decomposing the lexicographic product of the complete graph and the complete graph minus a 1-factor, with complement of the complete graph K-m, (that is K-n circle times (K-m) over bar and K-n - l circle times (K-m) over bar, respectively) into sunlet graphs of order twice a prime. (C) 2016 Kalasalingam University. Publishing Services by Elsevier B.V.