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 S⊆V is a dominating set of G, if every vertex in V∖S 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(m−1), G(m−2), and G(m−3). 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 -