The Reflexive H-Strength on Some Graphs

Abstract

Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G).  The irregular reflexive -labeling is defined by the function  and  such that  if  and  if , where  max . The irregular reflexive  labeling is called an -irregular reflexive -labeling of the graph  if every two different sub graphs  and  isomorphic to  it holds , where  for the sub graph . The minimum  for graph  which has an -irregular reflexive -labelling is called the reflexive  strength of the graph  and denoted by . In this paper we determine the lower bound of the reflexive  strength of some subgraphs,  on , the sub graph  on  the sub graph  on  and the sub graph  on .