ON CO-SEGREGATED GRAPHS

Abstract

A connected graph G is totally segregated if every pair of adjacent vertices has distinct degrees. In this article, the class of graphs called co-segregated graphs which are complements of totally segregated graphs is discussed. The maximum size of connected totally segregated graph is found by finding minimum size of a large class of co-segregated graphs. We provide an algorithm to find minimum size of co-segregated graph. A construction of co-segregated graph of order n with minimum size is also described.