Strong Split Monophonic Number of a Graph

Abstract

In this paper we introduce a new graph theoretic parameter, strong split monophonic number of a graph as follows. A set  is a strong split monophonic set of , if is a monophonic set and subgraph induced by  is totally disconnected. The strong split monophonic number of a graph  is denoted by   , is the minimum cardinality of the strong split monophonic set of  . Here we investigate the strong split monophonic number for some special graphs. Also we have shown that, for integers   with   , there exists a connected graph  of order  such that  . For any three integers  with  there exist a connected graph.