The paper investigates properties of a special graph $S(n,f)$ defined as follows: an $(f,2)$-graph is a (multi)graph with each degree either $f$ or $2$. An insertion of a vertex of degree $2$ in a graph is a replacement of an edge with a path of length $2$, and a suppression of a vertex $v$ of degree $2$ is a replacement of the pair of $v$-adjacent edges by a single edge. Then, the vertex set of graph $S(n,f)$ is the set of $(f,2)$ graphs with at most $n$ nodes and a pair of graphs $\{G,H\}$ is an edge in $S(n,f)$ if and only if $H$ can be obtained from $G$ by either an insertion or a suppression. Based on the graph $S(n,f)$, a Markov chain is defined and studied. Relation to chemical studies is mentioned.
Reviewer: Petr Kolman (Praha)