On the generation of minimal graph extensions by the method of canonical representatives

A graph $G^*$ is a $k$-vertex (edge) extension of a graph $G$ if every graph obtained by removing any $k$ vertices (edges) from $G^*$ contains $G$. A $k$-vertex (edge) extension $G^*$ of graph $G$ is said to be minimal if it contains minimum possible vertices and has the minimum number of edges among all $k$-vertex (edge) extension of graph $G$. The paper proposes an algorithm for generating all non-isomorphic minimal vertex (edge) $k$-extensions of a given graph with isomorphism rejection technique by using method of generating canonical representatives.