Document Type: Regular Paper
Department of Mathematics, University of Tafresh, Tafresh, Iran
School of Mathematics, Institute for Research in Fundamental Sciences (IPM) Tehran, Iran, P.O. Box 19395-5746
Shahab Danesh Institute of Higher Education, Qom, Iran
Let , be a graph with vertex set of order and edge set . A -dominating set of is a subset such that each vertex in has at least neighbors in . If is a vertex of a graph , the open -neighborhood of , denoted by , is the set , . is the closed -neighborhood of . A function 1, 1 is a signed distance- dominating function of , if for every vertex , Σ 1. The signed distance--domination number, denoted by ,, is the minimum weight of a signed distance--dominating function of . In this paper, we give lower and upper bounds on , of graphs. Also, we determine the signed distance--domination number of graph , (the graph obtained from the disjoint union by adding the edges , ) when 2.