Presented by: 
Professor Abdollah Khodkar (West Georgia)
Date: 
Thu 2 Feb, 2:00 pm
Venue: 
442 in Priestley (67)

The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having an end-vertex in common with e. Let f be a function on E(G), the edge set of G, into the set {-1,1} and let k1 be an integer. If ΣxN[e]f(x) ≥ k for each edge e ∈ E(G), then f is called a signed edge k-domination function (SEkDF) of G. The signed edge k-domination number γ’sk(G) of G is defined as

γ’sk(G) = min{ΣeE(G)f(e) | f is an SEkDF of G}

In this presentation, we calculate the signed edge k-domination numbers for complete graphs and complete bipartite graphs. We then show that, for any simple graph G,

γ’sk(G) ≥ |V (G)| - | E(G)| + - 1, 

and characterize all graphs that achieve this lower bound. This generalizes the existing results for k = 1.