Abstract
It is a conjecture that in any unit disk graph $$G$$G, $$\alpha (G) \le 3 \cdot \gamma _c(G) + 3$$?(G)≤3·?c(G)+3 where $$\alpha (G)$$?(G) is the size of the maximum independent set in $$G$$G and $$\gamma _c(G)$$?c(G) is the size of minimum connected dominating set in $$G$$G. In this paper, we show that in any unit disk graph $$G$$G, $$\alpha (G) \le 3.399 \cdot \gamma _c(G) + 4.874$$?(G)≤3.399·?c(G)+4.874. Currently, this is the best-known bound.
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