The Connected Detour Edge Semi Toll Number of a Graph

Abstract

A detour edge semi toll set of a connected graph  is called a connected detour edge semi toll set of  if the induced subgraph  is connected. The minimum cardinality of a connected detour semi toll set of  is the connected detour semi toll number and is denoted by  Any connected detour semi Euler set of cardinality  is called a -set of Some general properties satisfied by this concept are studied . Some standard graphs are determined.It is shown that for every pair of  and  of integers with there exists a connected graph  such that and .