Γ -Paired dominating graphs of some paths
Pannawat Eakawinrujee, Nantapath Trakultraipruk · MATEC Web of Conferences · 2018
A paired dominating set of a graphG = (V(G),E(G))is a setDof vertices ofGsuch that every vertex is adjacent to some vertex inD, and the subgraph ofGinduced byDcontains a perfect matching. The upper paired domination number ofG, denoted by Γpr(G) is the maximum cardinality of a minimal paired dominating set ofG. A paired dominatin set of cardinality Γpr(G) is called a Γpr(G) -set. The Γ -paired dominating graph of G, denoted by ΓPD(G), is the graph whose vertex set is the set of all Γpr(G) -sets, and two Γpr(G) -sets are adjacentin ΓPD(G) if one can be obtained from the other by removing one vertex and adding another vertex ofG. In this paper, we present the Γ-paired dominating graphs of some paths.