CO-SEGREGATED POLYNOMIAL OF GRAPHS

Abstract

A graph $G$ is co-segregated if $\text{deg}_G(x)=\text{deg}_G(y),$ then $xy \in E(G)$. The co-segregated polynomial of a graph $G$ of order $n$ is given by $CoS(G,x)=\sum_{k=1}^{n}C(k)x^k$,  where $C(k)$  is the number of co-segregated subgraphs of $G$ of order $k$. We characterize a co-segregated subgraph of a graph and also of a graph under some binary operations. Using these characterizations, we obtain co-segregated polynomials of such graphs.