Signed edge domination numbers of complete tripartite graphs: Part One

Abstract

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 / be a function on E(G), the edge set of G, into the set {-1,1}. If ΣxϵN[e] f(x) ≥ 1 for each edge e ϵ E(G), then f is called a signed edge dominating function of G. The signed edge domination number y¹ _s(G) of G is defined as y_s(G) = min{ΣeϵE(G) f(e) | f is a signed edge dominating function of G}. In this paper, we find the signed edge domination number for the complete tripartite graph K_m,n,p, where 1 ≤ m≤n≤p≤m + n. © 2017 Utilitas Mathematica Publishing Inc.. All rights reserved.