• SOME RESULTS ON COMPLETELY EXTENDABLE AND WEIGHTED EXTENDABLE GRAPHS

Abstract

In this paper we study certain properties of completely extendable graphs. In [3] we define an extension in a graph  by adding edges in a particular pattern. Certain graphs become complete after the finite extensions. Such graphs are called completely extendable graphs. Necessary and sufficient condition for a graph to be completely extendable is given in [3]. Here we discuss theorems related to completely extendable graphs. We also consider weighted graph and define extensions on weighted graph. We also give characterisation for a weighted graph to be completely weighted extendable. Next we consider  which is not completely extendable. We define deficiency number of a graph which is not completely extendable and give a particular pattern of extension to make such graphs complete.