Secure Distance Matrix Domination Graphs

Abstract

Let D_SDM (G)=(V (D_SDM) ,E 〖(D〗_SDM)) become an undirected, fundamental graph. Predominance in graphical representations is a specific area of theory pertaining to graphs the fact that has been thoroughly explored. A subset D_SDM (S) in the event every vertex within D_SDM (S) has become either contained within D_SDM (S) or closest to a separate the vertices in D_SDM (S), subsequently the overall quantity of points that compose the graph's structure has been identified as the dominant set. This article determines novel domination outcomes in graphs known as secure distance matrix domination. A dominating set of D_SDM (S) regarding D_SDM (G ) can be considered to have the attributes of a stable, dominant group of D_SDM (G ) once it has just one available. vertex D_SDM (u) ∈(D_SDM ( V) \ D_SDM ( S)) with respect to D_SDM (uv) ∈(D_SDM ( E)as well as ( D_SDM (S)) \( D_SDM {v} ∪ D_SDM {u})  has become a dominant set have been D_SDM that includes each points D_SDM (v) ∈D_SDM ( S). The issue is minimally secure determining a set that dominates of D_SDM (G)  using a minimum secure cardinality is the definition of dominance.  A few secure distance matrix dominant set theorems are outlined.