On bi-domination in graphs

الملخص EN

A dominating set is a bi-dominating set in a graph, if every vertex in this set, dominates exactly two vertices that, do not belong to the dominating set.

In thiswork, five new definitions of domination have been presented, which they area modified versions of bi-domination: “independent bi-domination; total bidomination, connected bi-domination, restrained domination, and complementarytree bi-domination”.

Upper and lower bounds are determined for the size of graphshaving these parameters.