TY - JOUR A2 - Shiu, Wai Chee AU - Alikhani, Saeid AU - Peng, Yee-Hock PY - 2013 DA - 2013/03/20 TI - Construction of Dominating Sets of Certain Graphs SP - 587196 VL - 2013 AB - Let G be a simple graph. A set SV is a dominating set of G, if every vertex in VS is adjacent to at least one vertex in S. We denote the family of dominating sets of a graph G with cardinality i by 𝒟(G,i). In this paper we introduce graphs with specific constructions, which are denoted by G(m). We construct the dominating sets of G(m) by dominating sets of graphs G(m1), G(m2), and G(m3). As an example of G(m), we consider 𝒟(Pn,i). As a consequence, we obtain the recursive formula for the number of dominating sets of G(m). SN - 2090-9837 UR - https://doi.org/10.1155/2013/587196 DO - 10.1155/2013/587196 JF - Journal of Discrete Mathematics PB - Hindawi Publishing Corporation KW - ER -