On the structure of (claw,bull)-free graphs

In this research, we determine the structure of (claw, bull)-free graphs. We show that every connected (claw, bull)-free graph is either an expansion of a path, an expansion of a cycle, or the complement of a triangle-free graph; where an expansion of a graph \(G\) is obtained by replacing its vertices with disjoint cliques and adding all edges between cliques corresponding to adjacent vertices of \(G\). This result also reveals facts about the structure of triangle-free graphs, which might be of independent interest.