In this paper, we revisited the concept of secure dominating set introduced by Cockayne et al. We characterized secure dominating set in terms of the concept of external private neighborhood of a vertex. Also we give necessary and sufficient conditions for connected graphs to have secure domination number equal to 2. We give some characterizations of the concept of secure domination in the joins K 1 + G and G + H, where G and H are connected non-complete graphs and then determine their corresponding secure domination numbers.

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