Bounds of the Signed Edge Domination Number of Complete Multipartite Graphs

A function f : E(G) → {-1, 1} is called a signed edge dominating function(SEDF for short) of G if ■, for every edge e ∈ E(G). ■ is called the weight of f. The signed edge domination number γs′(G) of G is the minimum weight among all signed edge dominating functions of G. In this paper, we initiate the study of this parameter for G a complete multipartite graph. We provide the lower and upper bounds of γs′(G) for G a complete r-partite graph with r even and all parts equal.