Actually chemical bonding is based on the Atomic number and electronic configuration.
And the main thing is valency which is based on the number of outer(valence) electrons.
Valency decides that how many bonds can be made by an atom . Thus if you ignore periodic table, you have to learn atomic number and electronic configuration of each and every element.
But i will suggest you to study periodic table , it will make it easy to understand chemical bonding.
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