Volume : 8, Issue : 5, May - 2019

TOTAL NONSPLIT GEODETIC NUMBER IN GRAPHS

Dr. A. Vijayalekshmi, Aksha S. S Jilu

Abstract :

The nonsplit geodetic set S of a graph G=(V(𝐺), E(𝐺)) is said to be total nonsplit geodetic set if the induced subgraph <S> has no isolated vertices. The minimum cardinality of a total nonsplit geodetic set in G is called total nonsplit geodetic number of G and is denoted by 𝑔𝑡𝑛𝑠(𝐺). In this paper we obtain a relationship between nonsplit geodetic number and the total nonsplit geodetic number of G. Also we find the total nonsplit geodetic number of some classes of graphs.