Recent Advancements in Graph Theory

18Unit Graphs having their Domination Number half their Order

Amit Kumar

Banasthali Vidyapith,Banasthali, Rajasthan (INDIA)E-mail: [e-mail]

Pranjali

University of Rajasthan,Jaipur, Rajasthan (INDIA)E-mail: [e-mail]

Mukti Acharya

Christ University,Bengaluru (INDIA)E-mail: [e-mail]

Pooja Sharma

Banasthali vidyapith,Banasthali, Rajasthan (INDIA)E-mail: [e-mail]

In this chapter, we characterize the rings for which the extrema in the inequality 1 ≤ γ(G(R)) ≤ n holds, where γ is the domination number of unit graph G(R). In the sequel, we determine the rings, whose unit graph has unique minimum dominating set. Further, we have considered the problem of characterizing the rings for which G(R) has either ...