Extreme Non-Split Geodesic Graphs

Abstract

 Here we study the new concept of extreme non-split geodesic graph in . The geodetic set  is called a non-split geodetic set, if the induced sub graph  is connected. The cardinality of a non-split geodetic set which is minimum is the non-split geodetic number . The extreme order  is the number of extreme vertices in a graph . The connected graph  is an extreme non-split geodesic graph if . Here we determine the extreme non-split geodesic graph  of  and  with  for the integers  and  with . Also we proved  and  for the integers ,  and  in a connected graph .