# Roman domination in graphs with minimum degree at least two and some forbidden cycles

@inproceedings{Sheikholeslami2021RomanDI, title={Roman domination in graphs with minimum degree at least two and some forbidden cycles}, author={Seyed Mahmoud Sheikholeslami and Mustapha Chellali and R. Khoeilar and Hossein Karami and Z. Shao}, year={2021} }

Let G = (V,E) be a graph of order n and let γR(G) and ∂(G) denote the Roman domination number and the differential of G, respectively. In this paper we prove that for any integer k ≥ 0, if G is a graph of order n ≥ 6k+9, minimum degree δ ≥ 2, which does not contain any induced {C5, C8, . . . , C3k+2}-cycles, then γR(G) ≤ (4k+8)n 6k+11 . This bound is an improvement of the bounds given in [E.W. Chambers, B. Kinnersley, N. Prince, and D.B. West, Extremal problems for Roman domination, SIAM J…

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