TITLE:
A Note on Edge-Domsaturation Number of a Graph
AUTHORS:
Devadhas Nidha, Murugan Kala
KEYWORDS:
Edge-Dominating Set; Edge-Domination Number; ds'- Critical; Edge-Domsaturation Number; Well Edge Dominated Graph
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.2 No.3,
July
18,
2012
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 – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.