@article{article_508451, title={Average weakly edge domination number in graphs}, journal={Communication in Mathematical Modeling and Applications}, volume={3}, pages={51–62}, year={2018}, author={Balci, Mehmet Ali and Dundar, Pinar}, keywords={Average weakly edge domination,edge distance}, abstract={ Communication is supposed to be continuous in a network design. It is important for a network to be tough so that  communication is not interrupted in case any damage. In this paper, it is investigated how to decide which graph model to choose,  when a selection is needed to make between different graphs to be used for a network model when all known vulnerability measures are same. We introduce the concept of the average weakly edge domination number of a graph as a new vulnerability measure. We establish relationships between the average weakly edge domination number and some other graph parameters, and the extreme values of given measure among all graphs and average weakly edge domination number for some families of graphs. Also a polynomial time  algorithm with complexity O ( n 3 ) is given. }, number={1}, publisher={Mustafa BAYRAM}