Forgotten domination, hyper domination and modified forgotten domination indices of graphs

Abstract

For each vertex υ ϵ V(G), the domination degree denoted by d_d (v) and defined as the number of minimal dominating sets of G which contains υ. In this paper, we will define new indices depend on domination degree called forgotten domination, hyper domination and modified forgotten domination indices. We establish these domination indices for some families of graphs. We also study some basic properties of these new indices lower and upper bound. We give exact values of forgotten domination, hyper domination and modified forgotten domination indices, including the join and corona product of graphs.

Subject Classification: (2020):

• 05C69-05C10

Keywords:

• Forgotten domination index
• Hyper domination index
• Modified forgotten domination domination degree
• Minimal domination set