Edge-Domsaturation Number of a Graph: A Mathematical Approach

Abstract

The edge-domsaturation number ds' (G) of a graph G=(V,E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds' (G)=q-\(\Delta\)' (G)   and investigate well-edge dominated graphs. We further define \(\lambda\)'-critical, \(\lambda\)'⁺-critical, ds'-critical, ds'-critical edges and study some of their properties.