TOTAL OUTER CONNECTED GEODETIC NUMBER OF SOME GRAPHS

Abstract

For a connected graph G of order at least two, a total outer connected geodetic set S of G is an outer connected geodetic set such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total outer connected geodetic set of G is the total outer connected geodetic number of G and is denoted by  In this paper, we determine bounds for it and characterize graphs which realize these bounds for some known graphs.