THE UPPER COMPLEMENT CONNECTED EDGE GEODETIC NUMBER OF A GRAPH

Abstract

A complement connected edge geodetic set of ???? is called a minimal complement connected edge geodetic set of ???? if no proper subset of ???? is a complement connected edge geodetic set of ????. The upper complement connected edge geodetic number ???????????????? + (????) is the maximum cardinality of a minimal complement connected edge geodetic set of ????. Some general properties satisfied by this concept are studied connected graphs of order p ≥ 3 with ???????????????? + (???? to be ???? − 1 is given. It is shown that for every pair of integers ???? and ???? with3 ≤ ???? ≤ ????, there exists a connected graph ???? with ????????????????(????) = ???? and ???????????????? + (????) = ????,where upper complement connected edge geodetic number of a graph.