The Neighborhood Set and the Neighbourhood Graph of the Nilpotent Cayley Graph of the Residue Class Ring (Zn, ⊕, ☉)
Levaku Madhavi1*, Tippaluri Nagalakshumma2, Jangiti Devendra3
1*. Associate Professor, Department of Applied Mathematics, Yogi Vemana University, Kadapa,-516005, A.P..
2. Assistant Professor, Department of Mathematics, Gouthami Engineering College, Proddatur,-516360, A.P..
3. Assistant Professor, Department of Mathematics, GITAM University, Bengaluru,-561203, Karnataka.
Abstract: The properties of the nilpotent Cayley graph associated with the set of nilpotent elements of the residue class ring (Zn, ⊕, ☉) and its vertex as well as edge domination parameters are studied by the authors. In this Paper the concepts of the neighborhood set, the neighborhood number and the neighborhood graph of the nilpotent Cayley graph G(Zn, N) are introduced and its basic properties are studied. Further it is established that the neighborhood graph G(Zn, N) is multi- partite and Hamiltonian.
Keywords: Nilpotent element, Nilpotent Cayley graph, Neighborhood graph of a graph.
Pages: 33 – 43 | Full PDF Paper