REGULAR EXTENSION OF GRAPHS

Regular graph is a graph in which all vertices have same degree. In this article, we find regular extension of graphs. For that, we introduce a regularizing sequence, which is a new tool for regularization of graphs. The process of constructing a regular graph that contains a given graph as a subgraph is called regularization of a graph. Regular extension of different classes of graphs is determined, and necessary conditions for a graph to be a regular-extendable graph are obtained. Some classes of regular extendable graphs and non-regular extendable graphs are identified.