Extensibility of Graphs

In this paper, the concepts of extension of a graph (digraph) and the extensible class ofgraphs (digraphs) have been introduced. the class of connected graphs as well as the class ofhamiltonian graphs which are extensible classes have also been proved. the classes of regular,eulerian, bipartite and trees graphs which are not extensible classes have also been proved. theconcept of extensibility number has been introduced as well as the characterization of regulargraphs (digraphs) which have extensibility number k. also the extensibility number ofeulerian graphs (digraphs) has been characterized.