Edge fixed monophonic concepts in graphs

Abstract

One concept that pervades all of graph theory is that of distance and distance is used in isomorphism testing graph operations hamiltonicity problems extremal problems on connectivity and diameter and convexity in graphs In this thesis we define and develop various concepts like the edge fixed monophonic number the upper edge fixed monophonic number and the forcing edge fixed monophonic number Further we investigate the connected edge fixed monophonic number the upper connected edge fixed monophonic number the forcing connected edge fixed monophonic number and the connected forcing connected edge fixed monophonic number of a graph Geodetic and monophonic concepts have many applications in location theory and convexity theory In Chapter 1 we collect the basic definitions and theorems which are needed for the subsequent chapters Let G be a non trivial connected graph with order p and size q A shortest u v path is called a u v geodesic T newline