A Characterization of Well-Covered Claw-Free Graphs Containing no \(4\)-Cycles

We show how a claw-free well-covered graph containing no \(4\)-cycle, with any given independence number \(m\), can be constructed by linking together \(m\) sub-graphs, each isomorphic to either \(K_2\) or \(K_3\). We show further that the only well-covered connected claw-free graphs containing no \(4\)-cycle that cannot be constructed in this way are \(K_1\), and the cycle graphs on \(5\) and \(7\) vertices respectively.