Co-Secure Regular Set Domination in Graphs

Abstract

Here, we initiate the new domination parameter called Co-secure regular set dominating set and is defined as: A Co-secure dominating set D of G is said to be a Co-secure regular set dominating set of G if for every set  there exists a non-void subset  then the subgraph  induced by  is regular and is denoted as CSRSD-set. The , the Co-secure regular set domination number of G is the cardinality of least CSRSD-set in G. Also, we obtained the  of various standard graphs and sharp bounds. Also characterize the  for all trees.